The Wolfram System has extensive graph computation capabilities, including finding paths, cycles, and subgraphs based on connectivity to direct support for traversal-based programming.

Operations and Modifications »

NeighborhoodGraph — graph neighborhood of some vertex, edge, etc.

Subgraph   ▪ GraphUnion   ▪ VertexAdd   ▪ VertexDelete   ▪ EdgeAdd   ▪ ...

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 Polynomials

TuttePolynomial — compute the Tutte polynomial of a graph

ChromaticPolynomial   ▪ FlowPolynomial

Graph Programming »

DepthFirstScan — scan a graph in depth-first order

BreadthFirstScan   ▪ AdjacencyMatrix   ▪ ...