Subsets and Permutations »

Permutations — get a list of permutations

BinarySubsets — enumerate subsets using binary representation

InversePermutation  ▪  KSubsets  ▪  RandomSubset  ▪  ToCycles  ▪  CycleIndex  ▪  ...

Partitions and Compositions »

Partitions — list partitions of a positive integer

Compositions — list all compositions of integer into parts

Tableaux — construct Young tableaux from integer partition

RandomPartition  ▪  FerrersDiagram  ▪  KSetPartitions  ▪  TableauClasses  ▪  ...

Graph Construction and Representations »

Graph, Edges, Vertices — basic graph elements

ShowGraph — display a graph

MakeGraph — construct a graph

GraphJoin — join two graphs

FromOrderedPairs  ▪  IncidenceMatrix  ▪  GraphOptions  ▪  RadialEmbedding

EdgeStyle  ▪  VertexStyle  ▪  Highlight  ▪  ...

Graph Properties »

DegreeSequence — list number of edges for each vertex

OrientGraph — find strongly connected orientation of a graph

ChromaticPolynomial — compute chromatic polynomial for a graph

NecklacePolynomial  ▪  HamiltonianCycle  ▪  ConnectedComponents  ▪  EdgeColoring

EdgeConnectivity  ▪  Girth  ▪  Bridges  ▪  ...

Graph Algorithms »

Dijkstra — find single-source shortest path

MinimumSpanningTree — find a minimum spanning tree of a graph

NetworkFlow — maximum flow through a graph

Isomorphism  ▪  Equivalences  ▪  ShortestPath

StableMarriage  ▪  DepthFirstTraversal  ▪  TransitiveClosure  ▪  ...