Degrees — list of degrees of vertices

InDegree — number of incoming edges

DegreeSequence — list number of edges for each vertex

GraphicQ — test if a list of integers is a graphic sequence

OutDegree  ▪  RealizeDegreeSequence  ▪  Spectrum

ListGraphs — list of nonisomorphic undirected graphs

NumberOfGraphs — number of nonisomorphic undirected graphs with vertices

GraphPolynomial  ▪  NumberOfDirectedGraphs

ListNecklaces — list distinct necklaces

NecklacePolynomial  ▪  NumberOfNecklaces

Cycles and Connectivity »

FindCycle — find cycle in a graph

HamiltonianCycle — find a Hamiltonian cycle

ConnectedComponents — get lists of connected components

OrientGraph  ▪  Bridges  ▪  ExtractCycles  ▪  TravelingSalesman  ▪  ...

Graph Coloring

TwoColoring — color vertices of a bipartite graph

ChromaticPolynomial — compute chromatic polynomial for a graph

ChromaticNumber — smallest number of colors to color the graph

MinimumVertexColoring — color a graph with the fewest colors

EdgeColoring  ▪  BipartiteQ  ▪  Backtrack

VertexColoring  ▪  BrelazColoring  ▪  EdgeChromaticNumber  ▪  PerfectQ

Graph Predicates

IdenticalQ — compare two graphs

IsomorphicQ — test if two graphs are isomorphic

PseudographQ — test if a graph is a pseudograph

AcyclicQ — test if a graph is acyclic

EmptyQ  ▪  CompleteQ  ▪  SimpleQ  ▪  MultipleEdgesQ  ▪  UndirectedQ  ▪  UnweightedQ

PlanarQ  ▪  CliqueQ  ▪  BipartiteQ  ▪  SelfLoopsQ  ▪  TriangleInequalityQ