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Combinatorica Package Guide
Graph Properties
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
ListGraphs list of nonisomorphic undirected graphs
NumberOfGraphs number of nonisomorphic undirected graphs with n vertices
ListNecklaces list distinct necklaces
FindCycle find cycle in a graph
HamiltonianCycle find a Hamiltonian cycle
ConnectedComponents get lists of connected components
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
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