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

VertexConnectivity  ▪  VertexConnectivityGraph