Cycles and Connectivity
As of Version 10, most of the functionality of the Combinatorica package is built into the Wolfram System. »
Graph Cycles
FindCycle — find a cycle in a graph
Girth — length of the shortest cycle
EulerianCycle — find an Eulerian tour on a graph
HamiltonianCycle — find a Hamiltonian cycle
ExtractCycles ▪ EulerianQ ▪ HamiltonianQ ▪ AcyclicQ
TravelingSalesman ▪ TravelingSalesmanBounds ▪ DeBruijnSequence
Graph Connectivity
ConnectedQ — test if a graph has only one component
ConnectedComponents — get lists of connected vertices
StronglyConnectedComponents ▪ WeaklyConnectedComponents
OrientGraph — find strongly connected orientation of a graph
ArticulationVertices — find cut points of a graph
Bridges — find bridges of a graph
BiconnectedComponents ▪ BiconnectedQ
EdgeConnectivity — minimal number of edges that disconnect the graph