Graphs & Networks

Graphs and networks are all around us, including technological networks (the internet, power grids, telephone networks, transportation networks, …), social networks (social graphs, affiliation networks, …), information networks (World Wide Web, citation graphs, patent networks, …), biological networks (biochemical networks, neural networks, food webs, …), and many more. Graphs provide a structural model that makes it possible to analyze and understand how many separate systems act together. 
The Wolfram Language provides state-of-the-art functionality for modeling, analyzing, synthesizing, and visualizing graphs and networks. Whether those graphs are small and diagrammatic or large and complex, the Wolfram Language provides numerous high-level functions for creating or computing with graphs. Graphs are first-class citizens in the Wolfram Language; they can be used as input and output and they are deeply integrated into the rest of the Wolfram Language.

(OrangeLink[Construction and Representation », paclet:guide/GraphConstructionAndRepresentation])

(RefLink[Graph, paclet:ref/Graph]) — graph object with vertex and edge properties

(RefLink[GraphData, paclet:ref/GraphData]), (RefLink[ExampleData, paclet:ref/ExampleData]) — curated collection of theoretical and empirical graphs

(OrangeLink[Visualization », paclet:guide/GraphVisualization])

(RefLink[Graph, paclet:ref/Graph]) — automatic visualization for graphs

(RefLink[HighlightGraph, paclet:ref/HighlightGraph]) — highlight elements in graphs

(OrangeLink[Properties and Measurements », paclet:guide/GraphPropertiesAndMeasurements])

(RefLink[GraphDistance, paclet:ref/GraphDistance]) — give the length of the shortest path between two vertices

(RefLink[IsomorphicGraphQ, paclet:ref/IsomorphicGraphQ]) — test whether two graphs are the same after vertex renaming

(OrangeLink[Computation on Graphs », paclet:guide/ComputationOnGraphs])

(RefLink[FindShortestPath, paclet:ref/FindShortestPath]) — find the shortest path from the source to a target

(RefLink[ConnectedComponents, paclet:ref/ConnectedComponents]) — give groups of vertices that are strongly connected

(OrangeLink[Social Network Analysis », paclet:guide/SocialNetworks])

(RefLink[FindClique, paclet:ref/FindClique]) — find cliques in a network

(RefLink[BetweennessCentrality, paclet:ref/BetweennessCentrality]) — give the fraction of shortest paths that pass through the actor