Mathematica provides state-of-the-art functionality for analyzing and synthesizing graphs and networks. Building on Mathematica's powerful numerical and symbolic capabilities, Mathematica 8 brings numerous high-level functions for computing with graphs.

• Modern extensible platform for graph computation and network analysis. »
• Support for directed, undirected, and weighted graphs.
• Hundreds of built-in Mathematica functions and standard graph algorithms.
• Direct support for random graph distributions. »
• Extensive collection of graph operations and modifications. »
• Support for set-theoretic and Boolean-based operations on graphs. »
• Selection of graph elements and subgraphs using Mathematica pattern language.
• Comprehensive collection of predicates for testing graph properties. »
• Efficient graph isomorphism testing. »
• Local and global structural properties, including components, covers, and matchings.
• 15+ metrics and centrality measures to characterize graphs and networks. »
• Efficient shortest path, cycle, and navigation functions. »
• Multi-paradigm approach to graph programming with matrix, optimization, and Boolean-based frameworks. »
• Generic BFS and DFS algorithms with a flexible programmatic interface. »
• Support of arbitrary properties for graph elements.
• Full integration of graphs and networks into Mathematica.

Study Urban Road Networks »	London Underground »	Solve Mazes »
Analyze Random Graph Models »	Vertex Degree Distributions »	Analyze Social Networks »
Symbolic Computation on Graphs  »	Subtract Random Neighborhoods »	Test Properties »
Convert to Matrix Representations »	Find an Isomorphism »	Degree Centrality in Social Networks »
Compute the Betweenness Centrality »	Centrality in Citation Networks »	Center, Periphery, and Distance Functions »
Visualize Eulerian Cycles »	Visualize Hamiltonian Cycles »	Color Cycle Decompositions »
Topological Sorting »	Shortest Paths »	Solve the Icosian Game »
Trip Planning »	Find K-Core Components »	Highlight Strongly Connected Components »
Find In- and Out-Components »	Edge Covers »	Independent Edge Sets  »
Highlight BFS and DFS trees »	Perform a Breadth-First Scan »	Perform a Depth-First Scan »
Study Properties of a Directed Graph »	Study Properties of an Undirected Graph »	Analyze Large and Complex Networks »

RELATED FUNCTIONS

Graph  UndirectedEdge  DirectedEdge  AdjacencyGraph  AdjacencyMatrix  IncidenceGraph  IncidenceMatrix  KirchhoffGraph  KirchhoffMatrix  WeightedAdjacencyGraph  WeightedAdjacencyMatrix  VertexCount  EdgeCount  VertexList  EdgeList  EdgeRules  VertexIndex  EdgeIndex  RandomGraph  UniformGraphDistribution  BernoulliGraphDistribution  BarabasiAlbertGraphDistribution  PriceGraphDistribution  WattsStrogatzGraphDistribution  DegreeGraphDistribution  Subgraph  NeighborhoodGraph  UndirectedGraph  DirectedGraph  ReverseGraph  SimpleGraph  IndexGraph  GraphComplement  GraphUnion  GraphIntersection  GraphDifference  GraphDisjointUnion  BooleanGraph  EdgeAdd  EdgeDelete  VertexAdd  VertexDelete  EdgeWeight  VertexWeight  HighlightGraph  GraphQ  EdgeQ  VertexQ  EmptyGraphQ  UndirectedGraphQ  DirectedGraphQ  LoopFreeGraphQ  SimpleGraphQ  WeightedGraphQ  IsomorphicGraphQ  AcyclicGraphQ  BipartiteGraphQ  ConnectedGraphQ  EulerianGraphQ  HamiltonianGraphQ  PathGraphQ  TreeGraphQ  VertexDegree  VertexInDegree  VertexOutDegree  GraphDistance  GraphDistanceMatrix  VertexEccentricity  GraphRadius  GraphDiameter  ClosenessCentrality  BetweennessCentrality  DegreeCentrality  EigenvectorCentrality  KatzCentrality  PageRankCentrality  HITSCentrality  FindShortestPath  GraphCenter  GraphPeriphery  FindEulerianCycle  FindHamiltonianCycle  ConnectedComponents  KCoreComponents  VertexComponent  VertexInComponent  VertexOutComponent  FindClique  FindVertexCover  VertexCoverQ  FindEdgeCover  EdgeCoverQ  FindIndependentVertexSet  IndependentVertexSetQ  FindIndependentEdgeSet  IndependentEdgeSetQ  Property  PropertyList  PropertyValue  DepthFirstScan  BreadthFirstScan  FindGraphIsomorphism  VertexReplace