what is graphical representation

• Math Article

Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

Thanks very much for the information

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

Introduction to Graphs

Table of Contents

15 December 2020                 

Read time: 6 minutes

Introduction

What are graphs?

What are the different types of data?

What are the different types of graphical representations?

The graph is nothing but an organized representation of data. It helps us to understand the data. Data are the numerical information collected through observation.

The word data came from the Latin word Datum which means “something given”

After a research question is developed, data is being collected continuously through observation. Then it is organized, summarized, classified, and then represented graphically.

Differences between Data and information: Data is the raw fact without any add on but the information is the meaning derived from data.

Introduction to Graphs-PDF

The graph is nothing but an organized representation of data. It helps us to understand the data. Data are the numerical information collected through observation. Here is a downloadable PDF to explore more.

• Line and Bar Graphs Application
• Graphs in Mathematics & Statistics

What are the different Types of Data?

There are two types of Data :

Quantitative

The data which are statistical or numerical are known as Quantitive data. Quantitive data is generated through. Quantitative data is also known as Structured data. Experiments, Tests, Surveys, Market Report.

Quantitive data is again divided into Continuous data and Discrete data.

Continuous Data

Continuous data is the data which can have any value. That means Continuous data can give infinite outcomes so it should be grouped before representing on a graph.

• The speed of a vehicle as it passes a checkpoint
• The mass of a cooking apple
• The time taken by a volunteer to perform a task

Discrete Data

Discrete data can have certain values. That means only a finite number can be categorized as discrete data.

• Numbers of cars sold at a dealership during a given month
• Number of houses in certain block
• Number of fish caught on a fishing trip
• Number of complaints received at the office of airline on a given day
• Number of customers who visit at bank during any given hour
• Number of heads obtained in three tosses of a coin

Differences between Discrete and Continuous data

• Numerical data could be either discrete or continuous
• Continuous data can take any numerical value (within a range); For example, weight, height, etc.
• There can be an infinite number of possible values in continuous data
• Discrete data can take only certain values by finite ‘jumps’, i.e., it ‘jumps’ from one value to another but does not take any intermediate value between them (For example, number of students in the class)

Qualitative

Data that deals with description or quality instead of numbers are known as Quantitative data. Qualitative data is also known as unstructured data. Because this type of data is loosely compact and can’t be analyzed conventionally.

Different Types of Graphical Representations

There are many types of graph we can use to represent data. They are as follows,

A bar graph or chart is a way to represent data by rectangular column or bar. The heights or length of the bar is proportional to the values.

A line graph is a type of graph where the information or data is plotted as some dots which are known as markers and then they are added to each other by a straight line.

The line graph is normally used to represent the data that changes over time.

A histogram graph is a graph where the information is represented along with the height of the rectangular bar. Though it does look like a bar graph, there is a fundamental difference between them. With the histogram, each column represents a range of quantitative data when a bar graph represents categorical variables.

The other name of the pie chart is a circle graph. It is a circular chart where numerical information represents as slices or in fractional form or percentage where the whole circle is 100%.

• Stem and leaf plot

The stem and leaf plot is a way to represents quantitative data according to frequency ranges or frequency distribution.

In the stem and leaf plot, each data is split into stem and leaf, which is 32 will be split into 3 stems and 2 leaves.

Frequency table: Frequency means the number of occurrences of an event. A frequency distribution table is a graph or chart which shows the frequency of events. It is denoted as ‘f’ .

Pictograph or Pictogram is the earliest way to represents data in a pictorial form or by using symbols or images. And each image represents a particular number of things.

According to the above-mentioned Pictograph, the number of Appels sold on Monday is 6x2=12.

• Scatter diagrams

Scatter diagram or scatter plot is a way of graphical representation by using cartesian coordinates of two variables. The plot shows the relationship between two variables. Below there is a data table as well as a Scattergram as per the given data.

What is the meaning of Graphical representation?

Graphical representation is a way to represent and analyze quantitive data. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables.

Principles of graphical representation

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin.

On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value.

When X-axis and y-axis intersected each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV.

The location on the coordinate plane is known as the ordered pair and it is written as (x,y). That means the first value will be on the x-axis and the second one is on the y-axis. When we will plot any coordinate, we always have to start counting from the origin and have to move along the x-axis, if it is positive then to the right side, and if it is negative then to the left side. Then from the x-axis, we have to plot the y’s value, which means we have to move up for positive value or down if the value is negative along with the y-axis.

In the following graph, 1st ordered pair (2,3) where both the values of x and y are positive and it is on quadrant I. 2nd ordered pair (-3,1), here the value of x is negative and value of y is positive and it is in quadrant II. 3rd ordered pair (-1.5, -2.5), here the value of x as well as y both are Negative and in quadrant III.

Methods of representing a frequency distribution

There are four methods to represent a frequency distribution graphically. These are,

• Smoothed Frequency graph
• Cumulative frequency graph or Ogive.
• Pie diagram.

Advantages and Disadvantages of Graphical representation of data

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represents it graphically.

You may also like:

• Graphing a Quadratic Function
• Empirical Relationship Between Mean, Median, and Mode

Not only in mathematics but almost in every field the graph is a very important way to store, analyze, and represents information. After any research work or after any survey the next step is to organize the observation or information and plotting them on a graph paper or plane. The visual representation of information makes the understanding of crucial components or trends easier.

A huge amount of data can be store or analyze in a small space.

The graphical representation of data helps to decide by following the trend.

A complete Idea: Graphical representation constitutes a clear and comprehensive idea in the minds of the audience. Reading a large number (say hundreds) of pages may not help to make a decision. Anyone can get a clear idea just by looking into the graph or design.

Graphs are a very conceptual topic, so it is essential to get a complete understanding of the concept. Graphs are great visual aids and help explain numerous things better, they are important in everyday life. Get better at graphs with us, sign up for a free trial . 

About Cuemath

Cuemath, a student-friendly mathematics and coding platform, conducts regular Online Classes for academics and skill-development, and their Mental Math App, on both iOS and Android , is a one-stop solution for kids to develop multiple skills. Understand the Cuemath Fee structure and sign up for a free trial.

Frequently Asked Questions (FAQs)

What is data.

Data are characteristics or information, usually numerical, that are collected through observation.

How do you differentiate between data and information?

Data is the raw fact without any add on but the information is the meaning derived from data.

What are the types of data?

There are two types of Data:

What are the ways to represent data?

Tables, charts and graphs are all ways of representing data , and they can be used for two broad purposes. The first is to support the collection, organisation and analysis of data as part of the process of a scientific study.

- Tables, charts and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organisation and analysis of data as part of the process of a scientific study.

What are the different types of graphs?

Different types of graphs include:

Graphical Representation

Graphical representation definition.

Graphical representation refers to the use of charts and graphs to visually display, analyze, clarify, and interpret numerical data, functions, and other qualitative structures. ‍

What is Graphical Representation?

Graphical representation refers to the use of intuitive charts to clearly visualize and simplify data sets. Data is ingested into graphical representation of data software and then represented by a variety of symbols, such as lines on a line chart, bars on a bar chart, or slices on a pie chart, from which users can gain greater insight than by numerical analysis alone. 

Representational graphics can quickly illustrate general behavior and highlight phenomenons, anomalies, and relationships between data points that may otherwise be overlooked, and may contribute to predictions and better, data-driven decisions. The types of representational graphics used will depend on the type of data being explored.

Types of Graphical Representation

Data charts are available in a wide variety of maps, diagrams, and graphs that typically include textual titles and legends to denote the purpose, measurement units, and variables of the chart. Choosing the most appropriate chart depends on a variety of different factors -- the nature of the data, the purpose of the chart, and whether a graphical representation of qualitative data or a graphical representation of quantitative data is being depicted. There are dozens of different formats for graphical representation of data. Some of the most popular charts include:

• Bar Graph -- contains a vertical axis and horizontal axis and displays data as rectangular bars with lengths proportional to the values that they represent; a useful visual aid for marketing purposes
• Choropleth -- thematic map in which an aggregate summary of a geographic characteristic within an area is represented by patterns of shading proportionate to a statistical variable
• Flow Chart -- diagram that depicts a workflow graphical representation with the use of arrows and geometric shapes; a useful visual aid for business and finance purposes
• Heatmap -- a colored, two-dimensional matrix of cells in which each cell represents a grouping of data and each cell’s color indicates its relative value
• Histogram – frequency distribution and graphical representation uses adjacent vertical bars erected over discrete intervals to represent the data frequency within a given interval; a useful visual aid for meteorology and environment purposes
• Line Graph – displays continuous data; ideal for predicting future events over time;  a useful visual aid for marketing purposes
• Pie Chart -- shows percentage values as a slice of pie; a useful visual aid for marketing purposes
• Pointmap -- CAD & GIS contract mapping and drafting solution that visualizes the location of data on a map by plotting geographic latitude and longitude data
• Scatter plot -- a diagram that shows the relationship between two sets of data, where each dot represents individual pieces of data and each axis represents a quantitative measure
• Stacked Bar Graph -- a graph in which each bar is segmented into parts, with the entire bar representing the whole, and each segment representing different categories of that whole; a useful visual aid for political science and sociology purposes
• Timeline Chart -- a long bar labelled with dates paralleling it that display a list of events in chronological order, a useful visual aid for history charting purposes
• Tree Diagram -- a hierarchical genealogical tree that illustrates a family structure; a useful visual aid for history charting purposes
• Venn Diagram -- consists of multiple overlapping usually circles, each representing a set; the default inner join graphical representation

Proprietary and open source software for graphical representation of data is available in a wide variety of programming languages. Software packages often provide spreadsheets equipped with built-in charting functions.

Advantages and Disadvantages of Graphical Representation of Data

Tabular and graphical representation of data are a vital component in analyzing and understanding large quantities of numerical data and the relationship between data points. Data visualization is one of the most fundamental approaches to data analysis, providing an intuitive and universal means to visualize, abstract, and share complex data patterns. The primary advantages of graphical representation of data are:

• Facilitates and improves learning: graphics make data easy to understand and eliminate language and literacy barriers
• Understanding content: visuals are more effective than text in human understanding
• Flexibility of use: graphical representation can be leveraged in nearly every field involving data
• Increases structured thinking: users can make quick, data-driven decisions at a glance with visual aids
• Supports creative, personalized reports for more engaging and stimulating visual  presentations 
• Improves communication: analyzing graphs that highlight relevant themes is significantly faster than reading through a descriptive report line by line
• Shows the whole picture: an instantaneous, full view of all variables, time frames, data behavior and relationships

Disadvantages of graphical representation of data typically concern the cost of human effort and resources, the process of selecting the most appropriate graphical and tabular representation of data, greater design complexity of visualizing data, and the potential for human bias.

Why Graphical Representation of Data is Important

Graphic visual representation of information is a crucial component in understanding and identifying patterns and trends in the ever increasing flow of data. Graphical representation enables the quick analysis of large amounts of data at one time and can aid in making predictions and informed decisions. Data visualizations also make collaboration significantly more efficient by using familiar visual metaphors to illustrate relationships and highlight meaning, eliminating complex, long-winded explanations of an otherwise chaotic-looking array of figures. 

Data only has value once its significance has been revealed and consumed, and its consumption is best facilitated with graphical representation tools that are designed with human cognition and perception in mind. Human visual processing is very efficient at detecting relationships and changes between sizes, shapes, colors, and quantities. Attempting to gain insight from numerical data alone, especially in big data instances in which there may be billions of rows of data, is exceedingly cumbersome and inefficient.

Does HEAVY.AI Offer a Graphical Representation Solution?

HEAVY.AI's visual analytics platform is an interactive data visualization client that works seamlessly with server-side technologies HEAVY.AIDB and Render to enable data science analysts to easily visualize and instantly interact with massive datasets. Analysts can interact with conventional charts and data tables, as well as big data graphical representations such as massive-scale scatterplots and geo charts. Data visualization contributes to a broad range of use cases, including performance analysis in business and guiding research in academia.

Guide On Graphical Representation of Data – Types, Importance, Rules, Principles And Advantages

What are Graphs and Graphical Representation?

Graphs, in the context of data visualization, are visual representations of data using various graphical elements such as charts, graphs, and diagrams. Graphical representation of data , often referred to as graphical presentation or simply graphs which plays a crucial role in conveying information effectively.

Principles of Graphical Representation

Effective graphical representation follows certain fundamental principles that ensure clarity, accuracy, and usability:Clarity : The primary goal of any graph is to convey information clearly and concisely. Graphs should be designed in a way that allows the audience to quickly grasp the key points without confusion.

• Simplicity: Simplicity is key to effective data visualization. Extraneous details and unnecessary complexity should be avoided to prevent confusion and distraction.
• Relevance: Include only relevant information that contributes to the understanding of the data. Irrelevant or redundant elements can clutter the graph.
• Visualization: Select a graph type that is appropriate for the supplied data. Different graph formats, like bar charts, line graphs, and scatter plots, are appropriate for various sorts of data and relationships.

Rules for Graphical Representation of Data

Creating effective graphical representations of data requires adherence to certain rules:

• Select the Right Graph: Choosing the appropriate type of graph is essential. For example, bar charts are suitable for comparing categories, while line charts are better for showing trends over time.
• Label Axes Clearly: Axis labels should be descriptive and include units of measurement where applicable. Clear labeling ensures the audience understands the data’s context.
• Use Appropriate Colors: Colors can enhance understanding but should be used judiciously. Avoid overly complex color schemes and ensure that color choices are accessible to all viewers.
• Avoid Misleading Scaling: Scale axes appropriately to prevent exaggeration or distortion of data. Misleading scaling can lead to incorrect interpretations.
• Include Data Sources: Always provide the source of your data. This enhances transparency and credibility.

Importance of Graphical Representation of Data

Graphical representation of data in statistics is of paramount importance for several reasons:

• Enhances Understanding: Graphs simplify complex data, making it more accessible and understandable to a broad audience, regardless of their statistical expertise.
• Helps Decision-Making: Visual representations of data enable informed decision-making. Decision-makers can easily grasp trends and insights, leading to better choices.
• Engages the Audience: Graphs capture the audience’s attention more effectively than raw data. This engagement is particularly valuable when presenting findings or reports.
• Universal Language: Graphs serve as a universal language that transcends linguistic barriers. They can convey information to a global audience without the need for translation.

Advantages of Graphical Representation

The advantages of graphical representation of data extend to various aspects of communication and analysis:

• Clarity: Data is presented visually, improving clarity and reducing the likelihood of misinterpretation.
• Efficiency: Graphs enable the quick absorption of information. Key insights can be found in seconds, saving time and effort.
• Memorability: Visuals are more memorable than raw data. Audiences are more likely to retain information presented graphically.
• Problem-Solving: Graphs help in identifying and solving problems by revealing trends, correlations, and outliers that may require further investigation.

Use of Graphical Representations

Graphical representations find applications in a multitude of fields:

• Business: In the business world, graphs are used to illustrate financial data, track performance metrics, and present market trends. They are invaluable tools for strategic decision-making.
• Science: Scientists employ graphs to visualize experimental results, depict scientific phenomena, and communicate research findings to both colleagues and the general public.
• Education: Educators utilize graphs to teach students about data analysis, statistics, and scientific concepts. Graphs make learning more engaging and memorable.
• Journalism: Journalists rely on graphs to support their stories with data-driven evidence. Graphs make news articles more informative and impactful.

Types of Graphical Representation

There exists a diverse array of graphical representations, each suited to different data types and purposes. Common types include:

1.Bar Charts:

Used to compare categories or discrete data points, often side by side.

2. Line Charts:

Ideal for showing trends and changes over time, such as stock market performance or temperature fluctuations.

3. Pie Charts:

Display parts of a whole, useful for illustrating proportions or percentages.

4. Scatter Plots:

Reveal relationships between two variables and help identify correlations.

5. Histograms:

Depict the distribution of data, especially in the context of continuous variables.

In conclusion, the graphical representation of data is an indispensable tool for simplifying complex information, aiding in decision-making, and enhancing communication across diverse fields. By following the principles and rules of effective data visualization, individuals and organizations can harness the power of graphs to convey their messages, support their arguments, and drive informed actions.

Download PPT of Graphical Representation

Video On Graphical Representation

FAQs on Graphical Representation of Data

What is the purpose of graphical representation.

Graphical representation serves the purpose of simplifying complex data, making it more accessible and understandable through visual means.

Why are graphs and diagrams important?

Graphs and diagrams are crucial because they provide visual clarity, aiding in the comprehension and retention of information.

How do graphs help learning?

Graphs engage learners by presenting information visually, which enhances understanding and retention, particularly in educational settings.

Who uses graphs?

Professionals in various fields, including scientists, analysts, educators, and business leaders, use graphs to convey data effectively and support decision-making.

Where are graphs used in real life?

Graphs are used in real-life scenarios such as business reports, scientific research, news articles, and educational materials to make data more accessible and meaningful.

Why are graphs important in business?

In business, graphs are vital for analyzing financial data, tracking performance metrics, and making informed decisions, contributing to success.

Leave a comment

Cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Related Posts

Best Google AdWords Consultants in India...

What is a Google Ads Consultant? A Google Ads Consultant is an expert who specializes in delivering expertise and advice on Google Ads, which is Google’s online advertising medium. Google Ads permits companies to develop and run ads that are visible on Google’s search engine and other Google platforms. The function of a Google Ads […]

Best PPC Consultants in India –...

What Is a PPC Consultant? A PPC consultant or a pay per click consultant is an expert who specializes in handling and optimizing PPC advertisement drives for companies. PPC is a digital marketing model where advertisers pay a price each time their ad is clicked. Standard PPC mediums include Bing Ads, Google Ads, and social media advertisement platforms like […]

Top 20 Generic Digital Marketing Interview...

1. What is Digital Marketing? Digital marketing is also known as online marketing which means promoting and selling products or services to potential customers using the internet and online platforms. It includes email, social media, and web-based advertising, but also text and multimedia messages as a marketing channel. 2. What are the types of Digital […]

Best Social Media Consultants in India...

What Is a Social Media Consultant? A social media advisor is a specialist who delivers direction, recommendation, and assistance linked to the usage of social media for people, companies, or associations. Their prime objective is to support customers effectively by employing social media platforms to gain specific objectives, such as improving brand awareness, entertaining target […]

Gaurav Mittal

Had a great time spent with some awesome learning at The Digital Education Institute. It really helped me to build my career and i am thankful to the institute for making me what i am today.

Company where our students are working

Enroll Now for 2 Hour Free Digital Marketing Class

Lorem Ipsum is simply dummy text of the printing and typesetting industry

Lorem Ipsum is simply dummy text of the printing and typesetting industry . Lorem Ipsum is simply dummy text of the printing and typesetting industry

• Privacy Policy

Buy Me a Coffee

Home » Graphical Methods – Types, Examples and Guide

Graphical Methods – Types, Examples and Guide

Table of Contents

Graphical Methods

Definition:

Graphical methods refer to techniques used to visually represent data, relationships, or processes using charts, graphs, diagrams, or other graphical formats. These methods are widely used in various fields such as science, engineering, business, and social sciences, among others, to analyze, interpret and communicate complex information in a concise and understandable way.

Types of Graphical Methods

Here are some of the most common types of graphical methods for data analysis and visual presentation:

Line Graphs

These are commonly used to show trends over time, such as the stock prices of a particular company or the temperature over a certain period. They consist of a series of data points connected by a line that shows the trend of the data over time. Line graphs are useful for identifying patterns in data, such as seasonal changes or long-term trends.

These are commonly used to compare values of different categories, such as sales figures for different products or the number of students in different grade levels. Bar charts use bars that are either horizontal or vertical and represent the data values. They are useful for comparing data visually and identifying differences between categories.

These are used to show how a whole is divided into parts, such as the percentage of students in a school who are enrolled in different programs. Pie charts use a circle that is divided into sectors, with each sector representing a portion of the whole. They are useful for showing proportions and identifying which parts of a whole are larger or smaller.

Scatter Plots

These are used to visualize the relationship between two variables, such as the correlation between a person’s height and weight. Scatter plots consist of a series of data points that are plotted on a graph and connected by a line or curve. They are useful for identifying trends and relationships between variables.

These are used to show the distribution of data across a two-dimensional plane, such as a map of a city showing the density of population in different areas. Heat maps use color-coded cells to represent different levels of data, with darker colors indicating higher values. They are useful for identifying areas of high or low density and for highlighting patterns in data.

These are used to show the distribution of data in a single variable, such as the distribution of ages of a group of people. Histograms use bars that represent the frequency of each data value, with taller bars indicating a higher frequency. They are useful for identifying the shape of a distribution and for identifying outliers or unusual data values.

Network Diagrams

These are used to show the relationships between different entities or nodes, such as the relationships between people in a social network. Network diagrams consist of nodes that are connected by lines that represent the relationship. They are useful for identifying patterns in complex data and for understanding the structure of a network.

Box plots, also known as box-and-whisker plots, are a type of graphical method used to show the distribution of data in a single variable. They consist of a box with whiskers extending from the top and bottom of the box. The box represents the middle 50% of the data, with the median value indicated by a line inside the box. The whiskers represent the range of the data, with any data points outside the whiskers indicated as outliers. Box plots are useful for identifying the spread and shape of a distribution and for identifying outliers or unusual data values.

Applications of Graphical Methods

Graphical methods have a wide range of applications in various fields, including:

• Business : Graphical methods are commonly used in business to analyze sales data, financial data, and other types of data. They are useful for identifying trends, patterns, and outliers, as well as for presenting data in a clear and concise manner to stakeholders.
• Science and engineering: Graphical methods are used extensively in scientific and engineering fields to analyze data and to present research findings. They are useful for visualizing complex data sets and for identifying relationships between variables.
• Social sciences: Graphical methods are used in social sciences to analyze and present data related to human behavior, such as demographics, survey results, and statistical analyses. They are useful for identifying trends and patterns in large data sets and for communicating findings to a broader audience.
• Education : Graphical methods are used in education to present information to students and to help them understand complex concepts. They are useful for visualizing data and for presenting information in a way that is easy to understand.
• Healthcare : Graphical methods are used in healthcare to analyze patient data, to track disease outbreaks, and to present medical information to patients. They are useful for identifying patterns and trends in patient data and for communicating medical information in a clear and concise manner.
• Sports : Graphical methods are used in sports to analyze and present data related to player performance, team statistics, and game outcomes. They are useful for identifying trends and patterns in player and team data and for communicating this information to coaches, players, and fans.

Examples of Graphical Methods

Here are some examples of real-time applications of graphical methods:

• Stock Market: Line graphs, candlestick charts, and bar charts are widely used in real-time trading systems to display stock prices and trends over time. Traders use these charts to analyze historical data and make informed decisions about buying and selling stocks in real-time.
• Weather Forecasting : Heat maps and radar maps are commonly used in weather forecasting to display current weather conditions and to predict future weather patterns. These maps are useful for tracking the movement of storms, identifying areas of high and low pressure, and predicting the likelihood of severe weather events.
• Social Media Analytics: Scatter plots and network diagrams are commonly used in social media analytics to track the spread of information across social networks. Analysts use these graphs to identify patterns in user behavior, to track the popularity of specific topics or hashtags, and to monitor the influence of key opinion leaders.
• Traffic Analysis: Heat maps and network diagrams are used in traffic analysis to visualize traffic flow patterns and to identify areas of congestion or accidents. These graphs are useful for predicting traffic patterns, optimizing traffic flow, and improving transportation infrastructure.
• Medical Diagnostics: Box plots and histograms are commonly used in medical diagnostics to display the distribution of patient data, such as blood pressure, heart rate, or blood sugar levels. These graphs are useful for identifying patterns in patient data, diagnosing medical conditions, and monitoring the effectiveness of treatments in real-time.
• Cybersecurity: Heat maps and network diagrams are used in cybersecurity to visualize network traffic patterns and to identify potential security threats. These graphs are useful for identifying anomalies in network traffic, detecting and mitigating cyber attacks, and improving network security protocols.

How to use Graphical Methods

Here are some general steps to follow when using graphical methods to analyze and present data:

• Identify the research question: Before creating any graphs, it’s important to identify the research question or hypothesis you want to explore. This will help you select the appropriate type of graph and ensure that the data you collect is relevant to your research question.
• Collect and organize the data: Collect the data you need to answer your research question and organize it in a way that makes it easy to work with. This may involve sorting, filtering, or cleaning the data to ensure that it is accurate and relevant.
• Select the appropriate graph : There are many different types of graphs available, each with its own strengths and weaknesses. Select the appropriate graph based on the type of data you have and the research question you are exploring. For example, a scatterplot may be appropriate for exploring the relationship between two continuous variables, while a bar chart may be appropriate for comparing categorical data.
• Create the graph: Once you have selected the appropriate graph, create it using software or a tool that allows you to customize the graph based on your needs. Be sure to include appropriate labels and titles, and ensure that the graph is clearly legible.
• Analyze the graph: Once you have created the graph, analyze it to identify patterns, trends, and relationships in the data. Look for outliers or other anomalies that may require further investigation.
• Draw conclusions: Based on your analysis of the graph, draw conclusions about the research question you are exploring. Use the graph to support your conclusions and to communicate your findings to others.
• Iterate and refine: Finally, refine your graph or create additional graphs as needed to further explore your research question. Iteratively refining and revising your graphs can help to ensure that you are accurately representing the data and that you are drawing the appropriate conclusions.

When to use Graphical Methods

Graphical methods can be used in a variety of situations to help analyze, interpret, and communicate data. Here are some general guidelines on when to use graphical methods:

• To identify patterns and trends: Graphical methods are useful for identifying patterns and trends in data, which may be difficult to see in raw data tables or spreadsheets. Graphs can reveal trends that may not be immediately apparent in the data, making it easier to draw conclusions and make predictions.
• To compare data: Graphs can be used to compare data from different sources or over different time periods. Graphical comparisons can make it easier to identify differences or similarities in the data, which can be useful for making decisions and taking action.
• To summarize data : Graphs can be used to summarize large amounts of data in a single visual display. This can be particularly useful when presenting data to a broad audience, as it can help to simplify complex data sets and make them more accessible.
• To communicate data: Graphs can be used to communicate data and findings to a variety of audiences, including stakeholders, colleagues, and the general public. Graphs can be particularly useful in situations where data needs to be presented quickly and in a way that is easy to understand.
• To identify outliers: Graphical methods are useful for identifying outliers or anomalies in the data. Outliers can be indicative of errors or unusual events, and may warrant further investigation.

Purpose of Graphical Methods

The purpose of graphical methods is to help people analyze, interpret, and communicate data in a way that is both accurate and understandable. Graphical methods provide visual representations of data that can be easier to interpret than tables of numbers or raw data sets. Graphical methods help to reveal patterns and trends that may not be immediately apparent in the data, making it easier to draw conclusions and make predictions. They can also help to identify outliers or unusual data points that may warrant further investigation.

In addition to helping people analyze and interpret data, graphical methods also serve an important communication function. Graphs can be used to present data to a wide range of audiences, including stakeholders, colleagues, and the general public. Graphs can help to simplify complex data sets, making them more accessible and easier to understand. By presenting data in a clear and concise way, graphical methods can help people make informed decisions and take action based on the data.

Overall, the purpose of graphical methods is to provide a powerful tool for analyzing, interpreting, and communicating data. Graphical methods help people to better understand the data they are working with, to identify patterns and trends, and to make informed decisions based on the data.

Characteristics of Graphical Methods

Here are some characteristics of graphical methods:

• Visual Representation: Graphical methods provide a visual representation of data, which can be easier to interpret than tables of numbers or raw data sets. Graphs can help to reveal patterns and trends that may not be immediately apparent in the data.
• Simplicity : Graphical methods simplify complex data sets, making them more accessible and easier to understand. By presenting data in a clear and concise way, graphical methods can help people make informed decisions and take action based on the data.
• Comparability : Graphical methods can be used to compare data from different sources or over different time periods. This can help to identify differences or similarities in the data, which can be useful for making decisions and taking action.
• Flexibility : Graphical methods can be adapted to different types of data, including continuous, categorical, and ordinal data. Different types of graphs can be used to display different types of data, depending on the characteristics of the data and the research question.
• Accuracy : Graphical methods should accurately represent the data being analyzed. Graphs should be properly scaled and labeled to avoid distorting the data or misleading viewers.
• Clarity : Graphical methods should be clear and easy to read. Graphs should be designed with the viewer in mind, using appropriate colors, labels, and titles to ensure that the message of the graph is conveyed effectively.

Advantages of Graphical Methods

Graphical methods offer several advantages for analyzing and presenting data, including:

• Clear visualization: Graphical methods provide a clear and intuitive visual representation of data that can help people understand complex relationships, trends, and patterns in the data. This can be particularly useful when dealing with large and complex data sets.
• Efficient communication: Graphical methods can help to communicate complex data sets in an efficient and accessible way. Visual representations can be easier to understand than numerical data alone, and can help to convey key messages quickly.
• Effective comparison: Graphical methods allow for easy comparison between different data sets, making it easier to identify trends, patterns, and differences. This can help in making decisions, identifying areas for improvement, or developing new insights.
• Improved decision-making: Graphical methods can help to inform decision-making by presenting data in a clear and easy-to-understand format. They can also help to identify key areas of focus, enabling individuals or teams to make more informed decisions.
• Increased engagement: Graphical methods can help to engage audiences by presenting data in an engaging and interactive way. This can be particularly useful in presentations or reports, where visual representations can help to maintain audience attention and interest.
• Better understanding: Graphical methods can help individuals to better understand the data they are working with, by providing a clear and intuitive visual representation of the data. This can lead to improved insights and decision-making, as well as better understanding of the implications of the data.

Limitations of Graphical Methods

Here are a few limitations to consider:

• Misleading representation: Graphical methods can potentially misrepresent data if they are not designed properly. For example, inappropriate scaling or labeling of the axes or the use of certain types of graphs can create a distorted view of the data.
• Limited scope: Graphical methods can only display a limited amount of data, which can make it difficult to capture the full complexity of a data set. Additionally, some types of data may be difficult to represent visually.
• Time-consuming : Creating graphs can be a time-consuming process, particularly if multiple graphs need to be created and analyzed. This can be a limitation in situations where time is limited or resources are scarce.
• Technical skills: Some graphical methods require technical skills to create and interpret. For example, certain types of graphs may require knowledge of specialized software or programming languages.
• Interpretation : Interpreting graphs can be subjective, and the same graph can be interpreted in different ways by different people. This can lead to confusion or disagreements when using graphs to communicate data.
• Accessibility : Some graphical methods may not be accessible to all audiences, particularly those with visual impairments. Additionally, some types of graphs may not be accessible to those with limited literacy or numeracy skills.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Probability Histogram – Definition, Examples and...

Substantive Framework – Types, Methods and...

Factor Analysis – Steps, Methods and Examples

Critical Analysis – Types, Examples and Writing...

Grounded Theory – Methods, Examples and Guide

Narrative Analysis – Types, Methods and Examples

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

2: Graphical Representations of Data

• Last updated
• Save as PDF
• Page ID 22222

In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

• 2.1: Introduction In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
• 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends.  A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
• 2.3: Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
• 2.4: Using Excel to Create Graphs Using technology to create graphs will make the graphs faster to create, more precise, and give the ability to use larger amounts of data. This section focuses on using Excel to create graphs.
• 2.5: Graphs that Deceive It's common to see graphs displayed in a misleading manner in social media and other instances. This could be done purposefully to make a point, or it could be accidental. Either way, it's important to recognize these instances to ensure you are not misled.
• 2.E: Graphical Representations of Data (Exercises) These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

tableau.com is not available in your region.

The Concise Encyclopedia of Statistics pp 236–237 Cite as

Graphical Representation

• Reference work entry

669 Accesses

Graphical representations encompass a wide variety of techniques that are used to clarify, interpret and analyze data by plotting points and drawing line segments, surfaces and other geometric forms or symbols.

The purpose of a graph is a rapid visualization of a data set. For instance, it should clearly illustrate the general behavior of the phenomenon investigated and highlight any important factors. It can be used, for example, as a means to translate or to complete a  frequency table .

Therefore, graphical representation is a form of data representation.

The concept of plotting a point in coordinate space dates back to at least the ancient Greeks, but we had to wait until the work of Descartes, René for mathematicians to investigate this concept.

According to Royston, E. (1970), a German mathematician named Crome, A.W. was among the first to use graphical representation in statistics . He initially used it as a teaching tool.

In his works Geographisch-statistische Darstellung...

This is a preview of subscription content, log in via an institution .

Buying options

• Available as PDF
• Read on any device
• Instant download
• Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Crome, A.F.W.: Ueber die Grösse und Bevölkerung der sämtlichen Europäischen Staaten. Weygand, Leipzig (1785)

Google Scholar  

Crome, A.F.W.: Geographisch-statistische Darstellung der Staatskräfte. Weygand, Leipzig (1820)

Fienberg, S.E.: Graphical method in statistics. Am. Stat. 33 , 165–178 (1979)

Article   Google Scholar  

Guerry, A.M.: Essai sur la statistique morale de la France. Crochard, Paris (1833)

Playfair, W.: The Commercial and Political Atlas. Playfair, London (1786)

Royston, E.: A note on the history of the graphical presentation of data. In: Pearson, E.S., Kendall, M. (eds.) Studies in the History of Statistics and Probability, vol. I. Griffin, London (1970)

Schmid, C.F.: Handbook of Graphic Presentation. Ronald Press, New York (1954)

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry.

(2008). Graphical Representation. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_174

Download citation

DOI : https://doi.org/10.1007/978-0-387-32833-1_174

Publisher Name : Springer, New York, NY

Print ISBN : 978-0-387-31742-7

Online ISBN : 978-0-387-32833-1

eBook Packages : Mathematics and Statistics Reference Module Computer Science and Engineering

Share this entry

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Talk to our experts

1800-120-456-456

• Graphical Representation of Data

Overview to Graphical Representation of Data

Mathematics is a field that deals with the gathering, analysis, interpretation, and presentation of numerical information in a very approach that's straightforward to know and compare. Business statistics, demographics,  statistics, and in other spheres of work graphical representation is used.

Tables and graphs show the area of information. People capture more information as soon as it is presented in a more attractive way than in any other format. Graphs are an effective way for showing comparisons between things completely as it has always been straightforward to explore the full information associated with different things.

The use of accurate charts to properly visualize and modify information sets is called image processing. The information is redirected to a computer image code and is represented by a variety of symbols, such as lines on a line chart, bar charts, or chart items, wherever users will gain more insight than numbers. analysis only.

Standalone images will help, predict and create advanced data-driven options by quickly depicting common behaviours and simple, unusual events, and interactions between information objects that cannot be marked. The categories of graphic images used are determined by the type of information being investigated.

Data charts are available in a variety of formats, as well as maps, diagrams, and graphs, and often contain written articles and fables to show the purpose of the chart, units of measurement, and variations, type of information, target chart and whether or not a general image in choosing the most effective chart.

Different Formats

1. Line Graphs - A line graph could be a visual illustration of how the worth of variables changes over time. Points with completely different variable values are coupled to create this graph. It may help evaluate information trends and predict future trends.

2. Graphs Bars - A bar chart could be a form of illustration of knowledge during which bars of a similar dimension are drawn on one axis (usually x-axis) with an equal area between them, showing dynamics. The length of the bars represents the variable values.

3. Histograms - this is often just like bar graphs, except that it supports the numbers' frequency instead of their actual values. The info is broken into intervals, and also the bars represent the frequency vary at intervals. That is, it calculates what percentage information values fall at intervals a given distance.

4. Pie Chart - A kind of graph during which information is pictured as a circular graph. A circle is split into sections, each representing a share of the full.

5. Heatmap - A heatmap could be a two-dimensional, matrix-coloured matrix during which every cell represents a group of knowledge and also the colour of every cell indicates its relative importance.

6. Purpose Map - Point map could be a contract answer for CAD and GIS for writing and an answer that edits the world and line of longitude inform variables to check information mapping.

Benefits of Graphics Illustration

The ability to investigate and perceive giant amounts of numerical information and also the relationship between information points needs table usage and graphical illustration of knowledge. One of the foremost vital ways to investigate information is to check information, providing a straightforward and comprehensive way to represent, visualize, and discuss advanced information patterns.

1. Graphics build information easier to interpret and clear language and learning barriers, simplifying and rising learning.

2. Content comprehension is easily done by human understanding.

3. Performance flexibility: Image displays may be employed in nearly any data-related field.

4. Increase organized thinking: visual aids enable users to create quicker, data-driven selections at a look.

5. Supports engaging and fun visual displays by permitting inventive, relevant reports.

6. Improves communication: reading graphics that emphasize key themes is quicker than reading a close line-by-line report.

7. Shows the full picture: all dynamics, time frames, information behaviour, and relationships are displayed in real-time.

Understanding and distinguishing patterns and trends within the ever-increasing flow of knowledge need a transparent visual illustration of the info. The employment of image displays permits speedy synchronous testing of massive information, which might facilitate the formation of foreseeable predictions and knowledgeable selections.

Graphical representation is a method of numerical data analysis. It shows a diagram of the relationship between knowledge, ideas, information, and concepts. It is easy to understand and one of the key learning strategies. The knowledge in a particular domain always depends on the type of information.

The visual representation forms are distinct. Some of the following are:

1. Line Graphs: Linear graphs display the continuous data and are useful for the prediction of future events over time.

2. Bar Graphs: Bar Graph is used for displaying the classification of details and compares data to the amounts by using solid bars.

3. Histograms: This chart, which uses bars to represent the frequency of numerical data, which are grouped in intervals, has the same width. Since all intervals are similar and continuous.

4. Line Plot: It shows the data frequency on a given line. 

5. Frequency Table: The table shows the number of data pieces within the interval given.

6. Circle Graph: Circle graph is a diagram which shows the relationships of the entire component. The circle shall be 100% and the categories occupied shall be represented by a certain percentage, such as 15%, 56%, etc.

7. Stem and Leaf Plot: Data from the lowest value to the highest value are arranged in the stem and leaf plot. The pictures of the lowest places in the sheets and the next places are the numbers.

8. Box and Whisker Plot: The diagram sums up the data in four sections. The graph is shown. Box and whisker indicate the range of information (distribution) and the medium data range.

General Rules for Graphical Representation of Data

There are some rules to display the data and information effectively in the graphical picture. They are as stated below:

Suitable Title: Ensure that the chart showing the topic of the presentation is given the appropriate title.

Measurement Unit: Make sure to mention the unit of measurement in the graph.

Proper Scale: Choose a proper scale to represent the data in an accurate manner.

Index: Index the corresponding colours, shades, rows, graphs format to better understand.

Data Sources: Include the information source at the bottom of the graph wherever necessary.

Keep it Simple: Construct a graph in an easy way that everyone can understand.

Neat: Choose the correct size, lettering, colours, etc. so that the chart is a visual aid to the screen.

Graphical Representation in Maths:

For mathematics, a diagram is a graph with statistical data represented by curves or lines across the coordinate point on its surface. It helps to research the relation between two variables whereby the change of the variable amount in respect of another variable can be calculated within a certain time interval. The distribution of the sequence and the frequency distribution can be analysed for a particular problem.

The data can be visually represented with two types of graphs. As listed below, they are as follows:

Time Series Graphs

Example: Line Graph.

Frequency Distribution Graphs

Example: Frequency Polygon Graph.

Principles of Graphical Representation:

All forms of graphical data representation are governed by algebraic principles. For diagrams, the co-ordinate axis is represented with two rows. The X-axis is a horizontal axis, while the Y-axis is indicated on the vertical axis. The intersecting point of two lines is called ‘O’. Take x-axis into account that the distance between origin and right is good and the distance between the source and left is good. The distance above the origin is also positive for the y-axis, and the distance below the origin is negative.

Generally, frequency distribution is represented in the following methods, namely:

Smoothed frequency graph.

Pie diagram.

Cumulative or ogive frequency graph.

Frequency Polygon.

Merits of Using Graphs.

Advantages of Graphical Representation of Data

The visual depiction of documents has different advantages that are as follows: 

This report is suitable for busy people because it emphasizes the subject of the report comfortably. It helps to avoid wasting time.

Data can be contrasted in terms of graphic representation. This kind of comparative analysis helps to understand and focus easily.

It takes a lot of time to correctly present concise data.

Corporate managers study the diagrams and very easily decide about the feasibility of the document.

A logical sequence is developed to clarify the public definition when tables, models, and graphs are used for data.

Poorly trained or illiterate people can easily understand graphics because a line-by-line diagram does not require a concise text.

Tables need less effort and less time for modelling, graphs, and pictures. This approach is always easy to understand the details.

Errors are reliable, insightful or descriptive. Since graphic figures, tablets and diagrams show less error and error usually.

The viewer gets a simple, complete idea from this depiction. There can be no place to judge 100 words.

Disadvantages of Graphical Representation of Data:

Document graphic representation is not unrestricted. The graphical representation problems of data or reports are as follows: 

The reports of graphical representation are costly because of the images, and colours. Combining content with human effort is costly in terms of visual layout.

It takes less time to represent a normal file, but the representation of the graph takes time since graphs and figures rely on more time.

Inconsistencies are all likely to occur due to the sophistication of the graphical representations. It leads to community awareness problems.

Graphs show the complete view of data that can keep anything from being kept secret.

Sample Example for Frequency polygon:

Here are the steps to be followed in order to find the frequency distribution of a polygon and it is graphically represented.

Get the frequency distribution and find the intervals of each group.

Mark the middle points along with the X-axis and y-axis frequencies.

At each mid-point, draw the points that are the same as the frequency.

Using lines in order to incorporate these details.

To complete the polygon, attach the point to the bottom or high-class points in the X-axis immediately at each end.

NCERT Study Material

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Computer science theory

Course: computer science theory   >   unit 1.

• Describing graphs

Representing graphs

• Challenge: Store a graph

Adjacency matrices

Adjacency lists, want to join the conversation.

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

8.3.1: Use and Misuse of Graphical Representations

• Last updated
• Save as PDF
• Page ID 63947

• The NROC Project

Learning Objectives

• Identify which type of graph best represents the data for a given situation.
• Explain how graphs can lead to misinterpretation of data.

Introduction

In addition to bar graphs , histograms , and circle graphs (pie charts), there are other graphs that statisticians use to represent data and analyze what it shows. But you have to be careful when creating and reading graphs. If they are not carefully created, they can be misleading, and sometimes people purposefully make them misleading.

Choosing a Graph

Choosing what type of graph to use to represent a specific data set takes some trial and error. And, sometimes, there is more than one appropriate type of graph you can use. What you choose depends on the way you want to present your data, as well as your own personal preferences. Modern spreadsheet programs like Excel are very flexible at creating different types of graphs; with only a couple clicks, you can view data represented as a bar graph, line graph, or circle graph. From there, you can choose which one best paints the picture you want to show.

Since there is often more than one way to graph a data set, let’s look at some examples and think about the different possibilities that are available to us.

A baseball writer wants to create a graph showing the total hits for the players with the greatest number of hits in the first half of the baseball season. These players have the following number of hits: 86, 88, 90, 90, 97, 99, 102, and 106. What type of graph should the writer use to represent the data?

A bar graph or pictograph would work best here. (A pictograph may be preferable for a small amount of data, and a bar graph may be preferable for a lot of data.)

The writer could use a stem-and-leaf plot to show the distribution of numerical data, but this kind of graph is not as effective at showing the relationship between each player and the number of hits that he has. A box-and-whisker plot, which shows the middle of a data set, is not useful here since the writer is interested in the hit totals, not the average number of hits or the spread of the data.

A statistician is collecting data on the frequency with which adults go to the dentist. She surveys 128 people and finds the following information.

• Less than 1 time per year: 28 respondents
• 1 time per year: 51 respondents
• 2 times per year: 42 respondents
• More than 2 times per year: 7 respondents

In a presentation to dentists, she especially wants to highlight the population that visits the dentist less than 1 time per year. What type of graph should she use to represent the data?

A circle graph is best, but a bar graph would also be acceptable.

As with the first example, stem-and-leaf plots and box-and-whisker plots are not useful here. The statistician is not interested in the average amount of times that a person goes to the dentist each year. A line graph would not be appropriate either, as the data is not continuous.

An amusement park planner wants to better understand the distribution of wait times that people experience while waiting for a popular ride. At the park one day, he asks 15 random people about the length of time they had to wait (in minutes).

12, 3, 2, 10, 12, 0, 2, 0, 8, 5, 4, 0, 7, 4, 6

What type of graph provides the best visual representation of this set of data: a circle graph, a box-and-whisker plot, or a bar graph?

An oceanographer wants to make a graph that shows the height (in centimeters) of a specific coral over the period of 2 years. Which type of graph is the most appropriate?

• Circle graph
• Box-and-whisker plot
• Stem-and-leaf plot

Incorrect. A circle graph is often used to show parts of a whole, not changes over time. The correct answer is a line graph.

Incorrect. A box-and-whisker plot is used to show the middle of a data set; it does not reveal much about growth over time. The correct answer is a line graph.

Correct. A line graph mapping height along the y-axis and time along the x-axis is the most appropriate type of graph for this situation.

Incorrect. A stem-and-leaf plot is used to show the spread of a data set; it does not reveal much about growth over time. The correct answer is a line graph.

Misleading Graphs

As you have seen, graphs provide a visual way to represent data sets. Pictures can be misleading, though, so you also need to know how to identify graphs that seem to show something different than what the data says. This may be due to carelessness or it may be done on purpose. Below are some general questions to keep in mind as you read graphs.

Questions to Consider when Reading Graphs

• Are the graphs labeled sufficiently?
• What is the scale?
• Does the graph show a full picture of the data, or only a select picture?

Look at the graph that follows. The title states “Average Salary for Adjunct Professors at Four Colleges,” and four bars appear on the graph. You can tell which colleges are being compared, but you are given no information about the scale that is being used. The graph makes it appear that the average salary for Adjunct Professors at Central College is much higher than that at Eastern College, but without a scale, you cannot know for certain. (You do know that the salary is higher; you just do not know how much higher.) To make this graph less misleading, a y-axis with salary information should be included.

Even when both axes are present and labeled correctly, graphical representations of data can be misleading. This is shown in the set of attendance graphs that follow.

In the graph on the left, the scale begins at 0 and goes to 20,000. The graph itself shows that attendance at Minneapolis Wildcats games has steadily increased each year since 2008, topping out in 2010 at just over 16,000.

Now look at the graph on the right. It appears to show that attendance at St. Paul Strikers’ games has increased even more dramatically: the bar for 2010 is more than twice as tall as that in 2008. From looking at these two graphs, you may conclude that the Strikers have been the more popular team recently, as the height of the bars seems to indicate that their attendance has grown faster than that of the Wildcats.

But notice something interesting: the scale of the Strikers graph is very different. It begins at 10,000! This paints a skewed picture of the data when compared with the Wildcats graph, which starts at 0. And by examining the actual data (the actual attendance, not just the height of the bars), you can tell that attendance is actually greater at the Wildcats games. In 2010, for instance, Wildcats attendance is a little over 16,000, while attendance at Strikers games is below 15,000.

This brings up an important point. When you are using graphs to compare data sets, the scales need to be consistent; otherwise, it is very difficult to compare the data itself. As you can tell from the two previous graphs, changing the scale of a graph can dramatically change the way it looks and the impression the graph makes.

A more honest representation of the attendance data can be found in a double-bar graph, where the attendance figures from both teams is mapped side-by-side using the same scale. Look at the results below. Now it is clear that the attendance for the Wildcats is greater than the attendance for the Strikers.

The circle graph here is another example of a misleading representation. The actual percentages of people who responded to each question are not available, and the viewer has to interpret the data based on the size of the sections. At first glance, this graph seems to be showing that a lot of voters seem to be favoring Candidate A, as the “Yes” section is very large.

Part of the reason why this section appears large is because the graph has been created so that it looks large. The circle graph is presented in three-dimensional form, and the data that is foremost in the graph (the “Yes” slice) appears the most prominent. The creator of this graph is hoping that this graph will make you think that Candidate A is very popular!

On closer inspection, though, the data does not seem to support this contention. Combining the “Yes” and “Probably Yes” sections is roughly equal to combining the “No” and “Probably No” sections, which means that the candidate is not as popular as this representation would suggest. In fact, someone who did not want this candidate to appear favorable could have represented the data using the next graph. Notice the different positions of the “No” and “Probably No” sections, as well as the consistent colors.

Notice how perspective and color make a difference in viewing and analyzing data!

Next is a more honest way of representing this data. In this graph, the circle graph is shown from above, and the actual percentages are included.

Results from a poll measuring a politician’s approval rating are shown in the table below.

Which of the following graphs is most misleading?

This line graph accurately displays the data; the axes are labeled appropriately, and the scale is from 0% to 100%. The graph shows that although there has been some up and down variation, the politician’s approval rating has stayed in the mid-50's. The correct answer is Graph B.

This graph uses a very small scale (10%, from 50% to 60%) and has eliminated the final two data points. This graph represents only a part of the data, and is designed to make the reader think that the politician is rated more favorably than he really is.

This bar graph accurately displays the data; the axes are labeled appropriately, and the scale is from 0% to 70%. The politician’s approval ratings look a bit higher in this graph than they do in Graph D, but there is nothing dishonest about this graph. The graph shows that although there has been some up and down variation, the politician’s approval rating has stayed in the mid-50's. The correct answer is Graph B.

This bar graph accurately displays the data; the axes are labeled appropriately, and the scale is from 0% to 100%, with 25% increments. It looks different than Graph C, but the data itself is not misleading: it is the scale of the data that is different. The correct answer is Graph B.

Graphs have a big impact on how you understand a set of data. Use an appropriate type of graph and you can communicate your data effectively; use the wrong type of graph, though, and your viewers may misunderstand the story you are trying to tell. When reading graphs in newspapers and online, be sure to look at the axes, the scale, and the presentation of the data itself. These can all help you identify if the graph is representing a data set fairly or unfairly.

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Published: 07 March 2024

Graph neural networks

• Gabriele Corso   ORCID: orcid.org/0000-0002-1963-8755 1   na1 ,
• Hannes Stark   ORCID: orcid.org/0000-0002-4463-326X 1   na1 ,
• Stefanie Jegelka   ORCID: orcid.org/0000-0002-6121-9474 1 , 2 ,
• Tommi Jaakkola 1 &
• Regina Barzilay 1  

Nature Reviews Methods Primers volume  4 , Article number:  17 ( 2024 ) Cite this article

1319 Accesses

45 Altmetric

Metrics details

• Computational biology and bioinformatics

iGraphs are flexible mathematical objects that can represent many entities and knowledge from different domains, including in the life sciences. Graph neural networks (GNNs) are mathematical models that can learn functions over graphs and are a leading approach for building predictive models on graph-structured data. This combination has enabled GNNs to advance the state of the art in many disciplines, from discovering new antibiotics and identifying drug-repurposing candidates to modelling physical systems and generating new molecules. This Primer provides a practical and accessible introduction to GNNs, describing their properties and applications to the life and physical sciences. Emphasis is placed on the practical implications of key theoretical limitations, new ideas to solve these challenges and important considerations when using GNNs on a new task.

This is a preview of subscription content, access via your institution

Access options

Access Nature and 54 other Nature Portfolio journals

Get Nature+, our best-value online-access subscription

24,99 € / 30 days

cancel any time

Subscribe to this journal

Receive 1 digital issues and online access to articles

92,52 € per year

only 92,52 € per issue

Rent or buy this article

Prices vary by article type

Prices may be subject to local taxes which are calculated during checkout

Code availability

Example code can be found at https://github.com/HannesStark/GNN-primer/blob/main/GNN-primer_HIV_classification.ipynb .

Gori, M., Monfardini, G. & Scarselli, F. A new model for learning in graph domains. In Proceedings 2005 IEEE International Joint Conference Neural Networks 729–734 (IEEE, 2005).

Merkwirth, C. & Lengauer, T. Automatic generation of complementary descriptors with molecular graph networks. J. Chem. Inf. Model. 45 , 1159–1168 (2005).

Article   CAS   PubMed   Google Scholar  

Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M. & Monfardini, G. The graph neural network model. IEEE Trans. Neural Netw. 20 , 61–80 (2008). Although the genealogy of the development is multifaced, this is often considered as the first instance of GNNs.

Article   PubMed   Google Scholar  

Bronstein, M. M., Bruna, J., Cohen, T. & Veličković, P. Geometric deep learning: grids, groups, graphs, geodesics, and gauges. Preprint at https://doi.org/10.48550/arXiv.2104.13478 (2021). Book with a very comprehensive introduction to the theoretical aspects behind GNNs and other geometric deep learning architectures.

Jegelka, S. Theory of graph neural networks: representation and learning. Preprint at https://doi.org/10.48550/arXiv.2204.07697 (2022).

Morgan, H. L. The generation of a unique machine description for chemical structures-a technique developed at chemical abstracts service. J. Chem. Doc. 5 , 107–113 (1965).

Article   CAS   Google Scholar  

Chandak, P., Huang, K. & Zitnik, M. Building a knowledge graph to enable precision medicine. Sci. Data 10 , 67 (2023).

Article   PubMed   PubMed Central   Google Scholar  

Fey, M. & Lenssen, J. E. Fast graph representation learning with PyTorch Geometric. Preprint at https://doi.org/10.48550/arXiv.1903.02428 (2019). PyTorch Geometric is the most widely used library to develop GNNs.

Wang, M. et al. Deep Graph Library: a graph-centric, highly-performant package for graph neural networks. Preprint at https://doi.org/10.48550/arXiv.1909.01315 (2019).

Yang, K. et al. Analyzing learned molecular representations for property prediction. J. Chem. Inf. Model. 59 , 3370–3388 (2019).

Article   CAS   PubMed   PubMed Central   Google Scholar  

Geiger, M. & Smidt, T. e3nn: Euclidean neural networks. Preprint at https://doi.org/10.48550/arXiv.2207.09453 (2022).

Hu, W. et al. Open Graph Benchmark: datasets for machine learning on graphs. Adv. Neural Inf. Process. Syst. 22118–22133 (NeurIPS Proceedings, 2020). OGB is the most widely used benchmark for GNNs with a wide variety of datasets, each with its own leaderboard.

Dummit, D. S. & Foote, R. M. Abstract algebra 7th edn (Wiley, 2004).

Xu, K., Hu, W., Leskovec, J. & Jegelka, S. How powerful are Graph Neural Networks? In International Conference on Learning Representations (ICLR, 2019). To our knowledge, this work, concurrently with [Mor+19], was the first to propose and use the analogy of GNNs to WL isomorphism test to study their expressivity.

Morris, C. et al. Weisfeiler and Leman go neural: higher-order graph neural networks. Proc. AAAI Conf. Artif. Intell. 33 , 4602–4609 (2019).

Google Scholar  

Vignac, C., Loukas, A. & Frossard, P. Building powerful and equivariant graph neural networks with structural message-passing. Adv. Neural Inf. Process. Syst. 33 , 14143–14155 (2020).

Abboud, R., Ceylan, I.I., Grohe, M. & Lukasiewicz, T. The surprising power of graph neural networks with random node initialization. In 30th International Joint Conferences on Artificial Intelligence 2112–2118 (International Joint Conferences on Artificial Intelligence Organization, 2021).

Sato, R., Yamada, M. & Kashima, H. Random features strengthen graph neural networks. In Proceedings of the 2021 SIAM International Conference on Data Mining 333–341 (Society for Industrial and Applied Mathematics, 2021).

Dwivedi, V. P. et al. Benchmarking graph neural networks. J. Mach. Learn. Res. 24 , 1–48 (2023).

MathSciNet   Google Scholar  

Beaini, D. et al. Directional graph networks. In Proceedings of the 38th International Conference on Machine Learning 748–758 (PMLR, 2021).

Lim, D. et al. Sign and basis invariant networks for spectral graph representation learning. In International Conference on Learning Representations (ICLR, 2023).

Keriven, N. & Vaiter, S. What functions can Graph Neural Networks compute on random graphs? The role of Positional Encoding. Preprint at https://doi.org/10.48550/arXiv.2305.14814 (2023).

Zhang, B., Luo, S., Wang, L. & He, D. Rethinking the expressive power of GNNs via graph biconnectivity. In International Conference on Learning Representations (ICLR, 2023).

Di Giovanni, F. et al. How does over-squashing affect the power of GNNs? Preprint at https://doi.org/10.48550/arXiv.2306.03589 (2023).

Razin, N., Verbin, T. & Cohen, N. On the ability of graph neural networks to model interactions between vertices. In 37th Conference on Neural Information Processing Systems (NeurIPS, 2023).

Bouritsas, G., Frasca, F., Zafeiriou, S. & Bronstein, M. M. Improving graph neural network expressivity via subgraph isomorphism counting. IEEE Trans. Pattern Anal. Mach. Intell. 45 , 657–668 (2023).

Sun, Z., Deng, Z.-H., Nie, J.-Y. & Tang, J. RotatE: knowledge graph embedding by relational rotation in complex space. Preprint at https://doi.org/10.48550/arXiv.1902.10197 (2019).

Abboud, R., Ceylan, I., Lukasiewicz, T. & Salvatori, T. BoxE: a box embedding model for knowledge base completion. Adv. Neural Inf. Process. Syst. 33 , 9649–9661 (2020).

Pavlović, A. & Sallinger, E. ExpressivE: a spatio-functional embedding for knowledge graph completion. In International Conference on Learning Representations (ICLR, 2023).

Veličković, P. et al. Graph attention networks. In International Conference on Learning Representations (ICLR, 2017). Graph attention networks are the first application of the idea of attention to graphs, and they are one of the most widely used architectures to date.

Corso, G., Cavalleri, L., Beaini, D., Liò, P. & Veličković, P. Principal neighbourhood aggregation for graph nets. Adv. Neural Inf. Process. Syst. 33 , 13260–13271 (2020).

Gasteiger, J., Weißenberger, S. & Günnemann, S. Diffusion improves graph learning. Adv. Neural Inf. Process. Syst. 32 , 13366–13378 (2019).

Gutteridge, B., Dong, X., Bronstein, M. & Di Giovanni, F. DRew: dynamically rewired message passing with delay. In International Conference on Machine Learning (eds Krause, A. et. al.) 12252–12267 (ICML, 2023).

Rampášek, L. et al. Recipe for a general, powerful, scalable graph transformer. Adv. Neural Inf. Process. Syst. 35 , 14501–14515 (2022).

Dwivedi, V. P. et al. Long range graph benchmark. Adv. Neural Inf. Process. Syst. 35 , 22326–22340 (2022).

Dwivedi, V. P. & Bresson, X. A generalization of transformer networks to graphs. Preprint at https://doi.org/10.48550/arXiv.2012.09699 (2020).

Kreuzer, D., Beaini, D., Hamilton, W., Létorneau, V. & Tossou, P. Rethinking graph transformers with spectral attention. Adv. Neural Inf. Process. Syst. 34 , 21618–21629 (2021).

Bodnar, C. et al. Weisfeiler and Lehman go topological: message passing simplicial networks. In Proceedings of the 38th International Conference on Machine Learning (eds Meila, M. & Zhang, T.) 1026–1037 (PMLR, 2021).

Bodnar, C. et al. Weisfeiler and Lehman go cellular: cw networks. Adv. Neural Inf. Process. Syst. 34 , 2625–2640 (2021).

Chamberlain, B. et al. Grand: graph neural diffusion. In Proceedings of the 38th International Conference on Machine Learning (eds Meila, M. & Zhang, T.) 1407–1418 (PMLR, 2021).

Chamberlain, B. et al. Beltrami flow and neural diffusion on graphs. Adv. Neural Inf. Process. Syst. 34 , 1594–1609 (2021).

Di Giovanni, F., Rowbottom, J., Chamberlain, B. P., Markovich, T. & Bronstein, M. M. Graph neural networks as gradient flows. Preprint at https://doi.org/10.48550/arXiv.2206.10991 (2022).

Rusch, T. K., Chamberlain, B., Rowbottom, J., Mishra, S. & Bronstein, M. Graph-coupled oscillator networks. In Proceedings of the 39th International Conference on Machine Learning (eds Chaudhuri, K. et al.) 18888–18909 (PMLR, 2022).

Schütt, K. et al. SchNet: a continuous-filter convolutional neural network for modeling quantum interactions. In NIPS’17: Proceedings of the 31st International Conference on Neural Information Processing Systems (eds von Luxburg, U. et al.) 992–1002 (Curran Associates Inc., 2017). SchNet is one of the earliest and most prominent examples of SE(3)-invariant GNNs.

Satorras, V. G., Hoogeboom, E. & Welling, M. E(n) equivariant graph neural networks. In Proceedings of the 38th International Conference on Machine Learning (eds Meila, M. & Zhang, T.) 9323–9332 (PMLR, 2021).

Dym, N. & Maron, H. On the universality of rotation equivariant point cloud networks. In International Conference on Learning Representations (ICLR, 2021).

Thomas, N. et al. Tensor field networks: rotation- and translation-equivariant neural networks for 3D point clouds. Preprint at https://doi.org/10.48550/arXiv.1802.08219 (2018).

Jing, B., Eismann, S., Suriana, P., Townshend, R. J. & Dror, R. Learning from protein structure with geometric vector perceptrons. In International Conference on Learning Representations (ICLR, 2021).

Gasteiger, J., Groß, J. & Günnemann, S. Directional message passing for molecular graphs. In Adv. Neural Inf. Process. Syst. (NeurIPS, 2020).

Gasteiger, J., Becker, F. & Günnemann, S. GemNet: universal directional graph neural networks for molecules. Adv. Neural Inf. Process. Syst. 34 , 6790–6802 (2021).

Baldassarre, F. & Azizpour, H. Explainability techniques for graph convolutional networks. Preprint at https://doi.org/10.48550/arXiv.1905.13686 (2019).

Schlichtkrull, M. S., De Cao, N. & Titov, I. Interpreting graph neural networks for NLP with differentiable edge masking. In International Conference on Learning Representations (ICLR, 2021).

Ying, Z., Bourgeois, D., You, J., Zitnik, M. & Leskovec, J. GNNExplainer: generating explanations for graph neural networks. Adv. Neural Inf. Process. Syst. 32 , 9240–9251 (2019).

PubMed   PubMed Central   Google Scholar  

Huang, Q., Yamada, M., Tian, Y., Singh, D. & Chang, Y. GraphLIME: local interpretable model explanations for graph neural networks. IEEE Trans. Knowl. Data Eng. 35 , 6968–6962 (2023).

Yuan, H., Tang, J., Hu, X. & Ji, S. XGNN: towards model-level explanations of graph neural networks. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining 430–438 (2020).

Yuan, H., Yu, H., Gui, S. & Ji, S. Explainability in graph neural networks: a taxonomic survey. IEEE Trans. Pattern Anal. Mach. Intell. 45 , 5782–5799 (2022).

Kakkad, J., Jannu, J., Sharma, K., Aggarwal, C. & Medya, S. A survey on explainability of graph neural networks. Preprint at https://doi.org/10.48550/arXiv.2306.01958 (2023).

Hirschfeld, L., Swanson, K., Yang, K., Barzilay, R. & Coley, C. W. Uncertainty quantification using neural networks for molecular property prediction. J. Chem. Inf. Model. 60 , 3770–3780 (2020).

Hsu, H. H.-H., Shen, Y., Tomani, C. & Cremers, D. What makes graph neural networks miscalibrated? In Adv. Neural Inf. Process. Syst. (NeurIPS, 2022).

Stadler, M., Charpentier, B., Geisler, S., Zügner, D. & Günnemann, S. Graph posterior network: Bayesian predictive uncertainty for node classification. Adv. Neural Inf. Process. Syst. 34 , 18033–18048 (2021).

Wang, X., Liu, H., Shi, C. & Yang, C. Be confident! towards trustworthy graph neural networks via confidence calibration. Adv. Neural Inf. Process. Syst. 34 , 23768–23779 (2021).

Huang, K., Jin, Y., Candes, E. & Leskovec, J. Uncertainty quantification over graph with conformalized graph neural networks. Preprint at https://doi.org/10.48550/arXiv.2305.14535 (2023).

Batzner, S. et al. E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nat. Commun. 13 , 2453 (2022).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Schlichtkrull, M. S. et al. Modeling relational data with graph convolutional networks. In The Semantic Web. ESWC 2018. Lecture Notes in Computer Science (eds Gangemi, A. et al.) 593–607 (Springer, Cham, 2018).

Sun, Q. et al. SUGAR: subgraph neural network with reinforcement pooling and self-supervised mutual information mechanism. In WWW ’21: Proceedings of the Web Conference 2021 (eds Leskovec, J. et al.) 2081–2091 (Association for Computing Machinery, 2021).

Sharma, K. et al. A survey of graph neural networks for social recommender systems. Preprint at https://doi.org/10.48550/arXiv.2212.04481 (2022).

Stokes, J. M. et al. A deep learning approach to antibiotic discovery. Cell 180 , 688–702.e13 (2020). Discovery of a novel antibiotic, halicin, via GNNs, one of the most prominent examples of the application of GNNs to scientific discovery.

Feinberg, E. N., Joshi, E., Pande, V. S. & Cheng, A. C. Improvement in ADMET prediction with multitask deep featurization. J. Med. Chem. 63 , 8835–8848 (2020).

Peng, Y. et al. Enhanced graph isomorphism network for molecular ADMET properties prediction. IEEE Access 8 , 168344–168360 (2020).

Article   Google Scholar  

Murphy, M. et al. Efficiently predicting high resolution mass spectra with graph neural networks. In Proceedings of the 40th International Conference on Machine Learning (eds Krause, A. et al.) 25549–25562 (PMLR, 2023).

Bevilacqua, B. et al. Equivariant subgraph aggregation networks. In International Conference on Learning Representations (ICLR, 2022).

Guo, M. et al. Hierarchical grammar-induced geometry for data-efficient molecular property prediction. In Proceedings of the 40th International Conference on Machine Learning (eds Krause, A. et al.) 12055–12076 (PMLR, 2023).

Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O. & Dahl, G. E. Neural message passing for quantum chemistry. In Proceedings of the 34th International Conference on Machine Learning (eds Precup, D. & Teh, Y. W.) 1263–1272 (PMLR, 2017). To our knowledge, this paper is the first to formalize the idea of message passing as presented in this Primer and proposes applications of GNNs to quantum chemistry, which remains one of the scientific fields in which GNNs have seen most applications.

Axelrod, S. & Gómez-Bombarelli, R. GEOM, energy-annotated molecular conformations for property prediction and molecular generation. Sci. Data 9 , 185 (2022).

Hermann, J., Schätzle, Z. & Noé, F. Deep-neural-network solution of the electronic Schrödinger equation. Nat. Chem. 12 , 891–897 (2020).

Gao, N. & Günnemann, S. Generalizing neural wave functions. In International Conference on Machine Learning 10708–10726 (ICML, 2023).

Kingma, D. P. & Welling, M. Auto-encoding variational bayes. In International Conferece on Learning Representations (ICLR, 2014).

Goodfellow, I. et al. Generative adversarial networks. Commun. ACM 63 , 139–144 (2020).

Mitton, J., Senn, H. M., Wynne, K. & Murray-Smith, R. A graph VAE and graph transformer approach to generating molecular graphs. Preprint at https://doi.org/10.48550/arXiv.2104.04345 (2021).

Jin, W., Barzilay, R. & Jaakkola, T. Junction tree variational autoencoder for molecular graph generation. In Proceedings of the 35th International Conference on Machine Learning (eds Dy, J. & Krause, A.) 2323–2332 (PMLR, 2018).

Jin, W., Barzilay, R. & Jaakkola, T. Hierarchical generation of molecular graphs using structural motifs. In Proceedings of the 37th International Conference on Machine Learning (eds Daumé, H. & Singh, A.) 4839–4848 (PMLR, 2020).

Vignac, C. & Frossard, P. Top-N: equivariant set and graph generation without exchangeability. In International Conference on Learning Representations (ICLR, 2022).

Jo, J., Lee, S. & Hwang, S. J. Score-based generative modeling of graphs via the system of stochastic differential equations. In Proceedings of the 39th International Conference on Machine Learning (eds Chaudhuri, K. et al.) 10362–10383 (PMLR, 2022).

Vignac, C. et al. DiGress: discrete denoising diffusion for graph generation. In International Conference on Learning Representations (ICLR, 2023).

Dauparas, J. et al. Robust deep learning–based protein sequence design using ProteinMPNN. Science 378 , 49–56 (2022).

Moon, S., Zhung, W., Yang, S., Lim, J. & Kim, W. Y. PIGNet: a physicsinformed deep learning model toward generalized drug–target interaction predictions. Chem. Sci. 13 , 3661–3673 (2022).

Xu, M. et al. GeoDiff: a geometric diffusion model for molecular conformation generation. In International Conference on Learning Representations (ICLR, 2022).

Jing, B., Corso, G., Chang, J., Barzilay, R. & Jaakkola, T. S. Torsional diffusion for molecular conformer generation. In Adv. Neural Inf. Process. Syst. (eds Sanmi, K. et al.) (NeurIPS, 2022).

Ingraham, J., Riesselman, A., Sander, C. & Marks, D. Learning protein structure with a differentiable simulator. In International Conference on Learning Representations (ICLR, 2019).

Jing, B. et al. EigenFold: generative protein structure prediction with diffusion models. Preprint at https://doi.org/10.48550/arXiv.2304.02198 (2023).

Corso, G., Stärk, H., Jing, B., Barzilay, R. & Jaakkola, T. S. DiffDock: diffusion steps, twists, and turns for molecular docking. In International Conference on Learning Representations (ICLR, 2023).

Ingraham, J. et al. Illuminating protein space with a programmable generative model. Nature 623 , 1070–1078 (2023).

Watson, J. L. et al. De novo design of protein structure and function with RFdiffusion. Nature 620 , 1089–1100 (2023).

Fu, X., Xie, T., Rebello, N. J., Olsen, B. D. & Jaakkola, T. Simulate time-integrated coarse-grained molecular dynamics with geometric machine learning. Preprint at https://doi.org/10.48550/arXiv.2204.10348 (2022).

Wang, W. et al. Generative coarse-graining of molecular conformations. In International Conference on Machine Learning 23213–23236 (ICML, 2022).

Yang, S. & Gomez-Bombarelli, R. Chemically transferable generative backmapping of coarse-grained proteins. In Proceedings of the 40th International Conference on Machine Learning (eds Krause, A. et al.) 39277–39298 (PMLR, 2023).

Huang, K. et al. Therapeutics data commons: machine learning datasets and tasks for drug discovery and development. In Proceedings of the Neural Information Processing Systems Track on Datasets and Benchmarks 1, NeurIPS Datasets and Benchmarks 2021 (NeurIPS, 2021).

Bajpai, A. K. et al. Systematic comparison of the protein-protein interaction databases from a user’s perspective. J. Biomed. Inform. 103 , 103380 (2020).

Tripp, A., Bacallado, S., Singh, S. & Hernández-Lobato, J. M. Tanimoto random features for scalable molecular machine learning. In Adv. Neural Inf. Process. Syst. (NeurIPS, 2023).

Stärk, H. et al. 3D Infomax improves GNNs for molecular property prediction. In Proceedings of the 39th International Conference on Machine Learning (eds Chaudhuri, K. et al.) 20479–20502 (PMLR, 2022).

Thakoor, S. et al. Large-scale representation learning on graphs via bootstrapping. In International Conference on Learning Representations (ICLR, 2022).

Devlin, J., Chang, M., Lee, K. & Toutanova, K. BERT: pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers) (eds Burstein, J. et al.) 4171–4186 (Association for Computational Linguistics, 2019).

Brown, T. et al. Language models are few-shot learners. Adv. Neural Inf. Process. Syst. 33 , 1877–1901 (2020).

Lin, Z. et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 379 , 1123–1130 (2023).

Article   ADS   MathSciNet   CAS   PubMed   Google Scholar  

Dosovitskiy, A. et al. An image is worth 16x16 words: transformers for image recognition at scale. In International Conference on Learning Representations (ICLR, 2021).

Misra, I. & van der Maaten, L. Self-supervised learning of pretext-invariant representations. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 6707–6717 (IEEE, 2020).

He, K., Fan, H., Wu, Y., Xie, S. & Girshick, R. Momentum Contrast for unsupervised visual representation learning. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 9726–9735 (IEEE, 2020).

Liu, Y. et al. Graph self-supervised learning: a survey. IEEE Trans. Knowl. Data Eng. 35 , 5879–5900 (2023).

Rusch, T. K., Bronstein, M. M. & Mishra, S. A survey on oversmoothing in graph neural networks. Preprint at https://doi.org/10.48550/arXiv.2303.10993 (2023).

Xu, K. et al. Representation learning on graphs with jumping knowledge networks. In Proceedings of the 35th International Conference on Machine Learning (eds Dy, J. & Krause, A.) 5453–5462 (PMLR, 2018).

Di Giovanni, F., Rowbottom, J., Chamberlain, B. P., Markovich, T. & Bronstein, M. M. Understanding convolution on graphs via energies. In Transact. Mach. Learn. Res. 2835–8856 (2023).

Rusch, T. K., Chamberlain, B. P., Mahoney, M. W., Bronstein, M. M. & Mishra, S. Gradient gating for deep multi-rate learning on graphs. In International Conference on Learning Representations (ICLR, 2023).

Alon, U. & Yahav, E. On the bottleneck of graph neural networks and its practical implications. In International Conference on Learning Representations (ICLR, 2021).

Topping, J., Di Giovanni, F., Chamberlain, B. P., Dong, X. & Bronstein, M. M. Understanding over-squashing and bottlenecks on graphs via curvature. In International Conference on Learning Representations (ICLR, 2022).

Dimitrov, R., Zhao, Z., Abboud, R. & Ceylan, I. I. PlanE: representation learning over planar graphs. Preprint at https://doi.org/10.48550/arXiv.2307.01180 (2023).

Hosseinzadeh, M. M., Cannataro, M., Guzzi, P. H. & Dondi, R. Temporal networks in biology and medicine: a survey on models, algorithms, and tools. Netw. Model. Anal. Health Inform. Bioinform. 12 , 10 (2023).

Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations (ICLR, 2017). Graph convolutional network was the architecture that set off the recent years of development of GNNs.

Download references

Acknowledgements

The authors thank R. Wu, S. Yang, D. Lim, A. Corso and M.-M. Troadec for their help in reviewing the manuscript before submission. The authors also thank B. Jing, F. Di Giovanni, J. Yim, C. Vignac and F. Faltings for useful discussions. This work was supported by the NSF Expeditions grant (award 1918839), the Machine Learning for Pharmaceutical Discovery and Synthesis (MLPDS) consortium, the DTRA Discovery of Medical Countermeasures Against New and Emerging (DOMANE) threats program, the DARPA Accelerated Molecular Discovery program, the NSF AI Institute CCF-2112665 and the NSF Award 2134795.

Author information

These authors contributed equally: Gabriele Corso, Hannes Stark.

Authors and Affiliations

CSAIL, MIT, Cambridge, MA, US

Gabriele Corso, Hannes Stark, Stefanie Jegelka, Tommi Jaakkola & Regina Barzilay

School of CIT, TU Munich, Munich, Germany

Stefanie Jegelka

You can also search for this author in PubMed   Google Scholar

Contributions

Introduction (R.B., G.C., H.S., S.J. and T.J.); Experimentation (R.B., G.C., H.S., S.J. and T.J.); Results (R.B., G.C., H.S., S.J. and T.J.); Applications (R.B., G.C., H.S., S.J. and T.J.); Reproducibility and data deposition (R.B., G.C., H.S. and S.J.); Limitations and optimizations (R.B., G.C., H.S., S.J. and T.J.); Outlook (R.B., G.C., H.S., S.J. and T.J.); overview of the Primer (all authors).

Corresponding authors

Correspondence to Gabriele Corso , Hannes Stark or Regina Barzilay .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Peer review

Peer review information.

Nature Reviews Methods Primers thanks Jiliang Tang; Siddhartha Mishra, who co-reviewed with Konstantin Rusch; and Rex Ying, who co-reviewed with Tinglin Huang, for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related links

ChEMBL: https://www.ebi.ac.uk/chembl/

Chemprop: https://github.com/chemprop/chemprop

Deep Graph Library: https://www.dgl.ai/

e3nn: https://e3nn.org/

PDBBind: http://www.pdbbind.org.cn/

Protein Data Bank: https://www.rcsb.org/

PyTorch Geometric: https://pytorch-geometric.readthedocs.io/en/latest/

Notation used in complexity theory to indicate how the worst-case runtime of an algorithm increases as the size of the input increases.

A simple example composition pattern is if molecule A binds to protein B and protein B is involved in the mechanism of disease C, then A is a potential candidate for C.

Subset of machine learning that uses artificial neural network models with multiple layers learning to automatically extract features and complex patterns from data.

Arrays of numbers produced by a deep learning model abstractly capture a model’s understanding of an object.

Information about the object under analysis that is passed as inputs to the model.

Task in which missing information in a knowledge graph is predicted based on existing relationships and patterns within the graph.

Fundamental component of graph neural networks that iteratively aggregates and updates the features from neighbouring nodes, enabling the propagation of information throughout the graph structure.

A planar graph is one that can be drawn on a 2D page without edges crossing each other.

The rectified linear unit (ReLU) is the most common type of non-linear function used in neural networks and has the simple form ReLU( x ) = max(0, x ).

Arrays of numbers that capture attributes of an object.

(Area under the curve of the receiver operator characteristic). A measure of the precision of a binary classifier that is informative in settings with unbalanced classes.

Core substructures within molecular graphs shared by multiple compounds that often have similar properties.

Setting that involves making predictions at inference time on a partially labelled graph, for a subset of the nodes within the graph. Models trained in a transductive setting do not generalize to other graphs.

Uncertainty refers to the lack of confidence or precision in a model’s prediction. Taking this ambiguity into account is often important in real-world applications of machine learning models.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Cite this article.

Corso, G., Stark, H., Jegelka, S. et al. Graph neural networks. Nat Rev Methods Primers 4 , 17 (2024). https://doi.org/10.1038/s43586-024-00294-7

Download citation

Accepted : 22 January 2024

Published : 07 March 2024

DOI : https://doi.org/10.1038/s43586-024-00294-7

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

• Data Structures
• Linked List
• Binary Tree
• Binary Search Tree
• Segment Tree
• Disjoint Set Union
• Fenwick Tree
• Red-Black Tree
• Advanced Data Structures
• Solve Coding Problems
• Graph Data Structure And Algorithms
• Introduction to Graphs - Data Structure and Algorithm Tutorials

Graph and its representations

• Types of Graphs with Examples
• Basic Properties of a Graph
• Applications, Advantages and Disadvantages of Graph
• Transpose graph
• Difference between graph and tree

BFS and DFS on Graph

• Breadth First Search or BFS for a Graph
• Depth First Search or DFS for a Graph
• Applications, Advantages and Disadvantages of Depth First Search (DFS)
• Applications, Advantages and Disadvantages of Breadth First Search (BFS)
• Iterative Depth First Traversal of Graph
• BFS for Disconnected Graph
• Transitive Closure of a Graph using DFS
• Difference between BFS and DFS

Cycle in a Graph

• Detect Cycle in a Directed Graph
• Detect cycle in an undirected graph
• Detect Cycle in a directed graph using colors
• Detect a negative cycle in a Graph | (Bellman Ford)
• Cycles of length n in an undirected and connected graph
• Detecting negative cycle using Floyd Warshall
• Clone a Directed Acyclic Graph

Shortest Paths in Graph

• How to find Shortest Paths from Source to all Vertices using Dijkstra's Algorithm
• Bellman–Ford Algorithm
• Floyd Warshall Algorithm
• Johnson's algorithm for All-pairs shortest paths
• Shortest Path in Directed Acyclic Graph
• Multistage Graph (Shortest Path)
• Shortest path in an unweighted graph
• Karp's minimum mean (or average) weight cycle algorithm
• 0-1 BFS (Shortest Path in a Binary Weight Graph)
• Find minimum weight cycle in an undirected graph

Minimum Spanning Tree in Graph

• Kruskal’s Minimum Spanning Tree (MST) Algorithm
• Difference between Prim's and Kruskal's algorithm for MST
• Applications of Minimum Spanning Tree
• Total number of Spanning Trees in a Graph
• Minimum Product Spanning Tree
• Reverse Delete Algorithm for Minimum Spanning Tree

Topological Sorting in Graph

• Topological Sorting
• All Topological Sorts of a Directed Acyclic Graph
• Kahn's algorithm for Topological Sorting
• Maximum edges that can be added to DAG so that it remains DAG
• Longest Path in a Directed Acyclic Graph
• Topological Sort of a graph using departure time of vertex

Connectivity of Graph

• Articulation Points (or Cut Vertices) in a Graph
• Biconnected Components
• Bridges in a graph
• Eulerian path and circuit for undirected graph
• Fleury's Algorithm for printing Eulerian Path or Circuit
• Strongly Connected Components
• Count all possible walks from a source to a destination with exactly k edges
• Euler Circuit in a Directed Graph
• Word Ladder (Length of shortest chain to reach a target word)
• Find if an array of strings can be chained to form a circle | Set 1
• Tarjan's Algorithm to find Strongly Connected Components
• Paths to travel each nodes using each edge (Seven Bridges of Königsberg)
• Dynamic Connectivity | Set 1 (Incremental)

Maximum flow in a Graph

• Max Flow Problem Introduction
• Ford-Fulkerson Algorithm for Maximum Flow Problem
• Find maximum number of edge disjoint paths between two vertices
• Find minimum s-t cut in a flow network
• Maximum Bipartite Matching
• Channel Assignment Problem
• Introduction to Push Relabel Algorithm
• Introduction and implementation of Karger's algorithm for Minimum Cut
• Dinic's algorithm for Maximum Flow

Some must do problems on Graph

• Find size of the largest region in Boolean Matrix
• Count number of trees in a forest
• A Peterson Graph Problem
• Clone an Undirected Graph
• Introduction to Graph Coloring
• Traveling Salesman Problem (TSP) Implementation
• Introduction and Approximate Solution for Vertex Cover Problem
• Erdos Renyl Model (for generating Random Graphs)
• Chinese Postman or Route Inspection | Set 1 (introduction)
• Hierholzer's Algorithm for directed graph
• Boggle (Find all possible words in a board of characters) | Set 1
• Hopcroft–Karp Algorithm for Maximum Matching | Set 1 (Introduction)
• Construct a graph from given degrees of all vertices
• Determine whether a universal sink exists in a directed graph
• Number of sink nodes in a graph
• Two Clique Problem (Check if Graph can be divided in two Cliques)

What is Graph Data Structure?

A Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(V, E) .

Representations of Graph

Here are the two most common ways to represent a graph :

Adjacency Matrix

Adjacency list.

An adjacency matrix is a way of representing a graph as a matrix of boolean (0’s and 1’s).

Let’s assume there are n vertices in the graph So, create a 2D matrix adjMat[n][n] having dimension n x n.

If there is an edge from vertex i to j , mark adjMat[i][j] as 1 . If there is no edge from vertex i to j , mark adjMat[i][j] as 0 .

Representation of Undirected Graph to Adjacency Matrix:

The below figure shows an undirected graph. Initially, the entire Matrix is ​​initialized to 0 . If there is an edge from source to destination, we insert 1 to both cases ( adjMat[destination] and adjMat [ destination]) because we can go either way.

Undirected Graph to Adjacency Matrix

Representation of Directed Graph to Adjacency Matrix:

The below figure shows a directed graph. Initially, the entire Matrix is ​​initialized to 0 . If there is an edge from source to destination, we insert 1 for that particular adjMat[destination] .

Directed Graph to Adjacency Matrix

An array of Lists is used to store edges between two vertices. The size of array is equal to the number of vertices (i.e, n) . Each index in this array represents a specific vertex in the graph. The entry at the index i of the array contains a linked list containing the vertices that are adjacent to vertex i .

Let’s assume there are n vertices in the graph So, create an array of list of size n as adjList[n].

adjList[0] will have all the nodes which are connected (neighbour) to vertex 0 . adjList[1] will have all the nodes which are connected (neighbour) to vertex 1 and so on.

Representation of Undirected Graph to Adjacency list:

The below undirected graph has 3 vertices. So, an array of list will be created of size 3, where each indices represent the vertices. Now, vertex 0 has two neighbours (i.e, 1 and 2). So, insert vertex 1 and 2 at indices 0 of array. Similarly, For vertex 1, it has two neighbour (i.e, 2 and 0) So, insert vertices 2 and 0 at indices 1 of array. Similarly, for vertex 2, insert its neighbours in array of list.

Undirected Graph to Adjacency list

Representation of Directed Graph to Adjacency list:

The below directed graph has 3 vertices. So, an array of list will be created of size 3, where each indices represent the vertices. Now, vertex 0 has no neighbours. For vertex 1, it has two neighbour (i.e, 0 and 2) So, insert vertices 0 and 2 at indices 1 of array. Similarly, for vertex 2, insert its neighbours in array of list.

Directed Graph to Adjacency list

Please Login to comment...

• graph-basics
• 10 Best Chegg Alternatives in 2024
• Devin AI: World’s First AI Software Engineer
• 12 Best FlexClip Alternatives & Competitors in 2024 [Free + Paid]
• What Is Trunk-Or-Treat?
• 30 OOPs Interview Questions and Answers (2024)

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Help | Advanced Search

Computer Science > Computer Vision and Pattern Recognition

Title: dynamic graph representation with knowledge-aware attention for histopathology whole slide image analysis.

Abstract: Histopathological whole slide images (WSIs) classification has become a foundation task in medical microscopic imaging processing. Prevailing approaches involve learning WSIs as instance-bag representations, emphasizing significant instances but struggling to capture the interactions between instances. Additionally, conventional graph representation methods utilize explicit spatial positions to construct topological structures but restrict the flexible interaction capabilities between instances at arbitrary locations, particularly when spatially distant. In response, we propose a novel dynamic graph representation algorithm that conceptualizes WSIs as a form of the knowledge graph structure. Specifically, we dynamically construct neighbors and directed edge embeddings based on the head and tail relationships between instances. Then, we devise a knowledge-aware attention mechanism that can update the head node features by learning the joint attention score of each neighbor and edge. Finally, we obtain a graph-level embedding through the global pooling process of the updated head, serving as an implicit representation for the WSI classification. Our end-to-end graph representation learning approach has outperformed the state-of-the-art WSI analysis methods on three TCGA benchmark datasets and in-house test sets. Our code is available at this https URL .

Submission history

Access paper:.

• Download PDF
• HTML (experimental)
• Other Formats

References & Citations

• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .