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As of Version 10, most of the functionality of the Combinatorica package is built into the Wolfram System. »

CompleteGraph a graph with an edge between each pair of vertices

RandomGraph construct a random graph

EmptyGraph   OddGraph   CirculantGraph   CompleteKPartiteGraph   Turan

Cycle a circular chain of edges

Star a tree-like graph with one vertex connected to all others

GridGraph graph with nodes on a grid

Wheel   Hypercube   ButterflyGraph   ShuffleExchangeGraph   DeBruijnGraph

Special Graphs

Harary smallest -connected graph with vertices

TutteGraph example of non-Hamiltonian graph

PetersenGraph   GeneralizedPetersenGraph   CageGraph

MeredithGraph   NoPerfectMatchingGraph   ThomassenGraph

KnightsTourGraph   ChvatalGraph   CoxeterGraph   FolkmanGraph

FranklinGraph   FruchtGraph   GrayGraph   GroetzschGraph

HerschelGraph   HeawoodGraph   LeviGraph   McGeeGraph   RobertsonGraph

UnitransitiveGraph   Uniquely3ColorableGraph   WaltherGraph

CubeConnectedCycle   MycielskiGraph

Platonic Solids

TetrahedralGraph   CubicalGraph   OctahedralGraph

IcosahedralGraph   DodecahedralGraph

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