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SOLUTIONS
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Functions
- AcyclicGraphQ
- AdjacencyGraph
- AdjacencyMatrix
- BetweennessCentrality
- BreadthFirstScan
- CompleteGraph
- ConnectedComponents
- DepthFirstScan
- DirectedEdge
- DirectedGraphQ
- EdgeAdd
- EdgeConnectivity
- EdgeStyle
- ExampleData
- FindClique
- FindEdgeCover
- FindGraphCommunities
- FindHamiltonianCycle
- FindIndependentEdgeSet
- FindKClan
- FindMaximumFlow
- FindPostmanTour
- FindShortestPath
- FindVertexCover
- Graph
- GraphData
- GraphDistance
- GraphLayout
- GraphUnion
- HamiltonianGraphQ
- HighlightGraph
- Import
- IsomorphicGraphQ
- KCoreComponents
- NeighborhoodGraph
- PageRankCentrality
- PropertyValue
- RandomGraph
- SocialMediaData
- Subgraph
- UndirectedEdge
- VertexAdd
- VertexDegree
- VertexDelete
- VertexEccentricity
- VertexLabels
- VertexStyle
- WeaklyConnectedComponents
- Related Guides
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.
Mathematica 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, Mathematica provides numerous high-level functions for creating or computing with graphs. Graphs are first-class citizens in Mathematica; they can be used as input and output and they are deeply integrated into the rest of the Mathematica system.
Learning ResourcesLearning Resources
Related Web Resources Training CoursesCommunity |
Featured ExamplesFeatured Examples |
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Analyzing Road Networks
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Apply Options of One Graph to Another
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Boolean Operations and Graphs
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Build Food Webs
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Build Semantic Networks
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Built-in Library of Edge Shapes
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Built-in Library of Vertex Shapes
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Centrality and Prestige of Florentine Families
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Cliques and Cohesive Groups
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Clustering in Small-World Networks
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Compare Centrality in Citation Networks
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Create Molecular Graphs
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Curated Collections of Graphs
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Display Planar Embeddings of Built-in Graphs
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Encode Structures into Graphs
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Find a Topological Ordering of Connected Graph Components
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Find People with More Influence in a Social Network
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Find the k-Core Components of a Graph
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Get Information on Graphs
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Graph Layouts
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Highlight Connected Components in a Directed Graph
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Highlight Graph Elements on BFS and DFS Trees
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Pack Disconnected Components
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Perform a Breadth-First Scan of a Graph
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Perform a Depth-First Scan of a Graph
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Powers of a Primitive Root
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Show Path with Arrows in a Matrix
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Solve the Icosian Game
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Structure of the Web
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Subtract Random Neighborhoods
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Visualize Eulerian Cycles
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Visualize Hamiltonian Cycles
ReferenceReference
Construction of Graphs »
Graph — construct a graph from vertices and edges
GraphData, ExampleData — curated collection of theoretical and empirical graphs
CompleteGraph ▪ RandomGraph ▪ AdjacencyGraph ▪ Import ▪ ...
Representation of Graphs »
Graph — graph object with vertex and edge properties
UndirectedEdge (
) ▪ DirectedEdge (
) ▪ ...
Social Network Analysis »
FindGraphCommunities — find well-connected communities
SocialMediaData ▪ BetweennessCentrality ▪ FindKClan ▪ ...
Styling, Labeling, and Layout »
HighlightGraph — highlight vertices, edges, or whole subgraphs
GraphLayout ▪ VertexStyle ▪ EdgeStyle ▪ VertexLabels ▪ ...
Operations and Modifications »
NeighborhoodGraph — graph neighborhood of some vertex, edge, etc.
Subgraph ▪ GraphUnion ▪ VertexAdd ▪ VertexDelete ▪ EdgeAdd ▪ ...
Predicates and Properties »
IsomorphicGraphQ — test whether two graphs are the same after vertex renaming
DirectedGraphQ ▪ AcyclicGraphQ ▪ HamiltonianGraphQ ▪ ...
Measures and Metrics »
GraphDistance — the length of the shortest path between two vertices
VertexDegree ▪ VertexEccentricity ▪ PageRankCentrality ▪ ...
Paths, Cycles and Flows »
FindMaximumFlow — find the maximum flow between two vertices
FindShortestPath ▪ FindHamiltonianCycle ▪ FindPostmanTour ▪ ...
Components and Connectivity »
ConnectedComponents — give groups of vertices that are strongly connected
WeaklyConnectedComponents ▪ KCoreComponents ▪ EdgeConnectivity ▪ ...
Cliques, Covers, and Independent Sets »
FindClique — find complete subgraphs
FindVertexCover ▪ FindEdgeCover ▪ FindIndependentEdgeSet ▪ ...
Graph Programming »
DepthFirstScan — scan a graph in depth-first order

