Graphs and Components

Graph — a graph object

Edges, Vertices — list of edges and vertices in a graph

M, V — number of edges and vertices in a graph

Graph Representations

ToOrderedPairs — get a list of edges

ToAdjacencyLists — represent a graph as adjacency lists

ToAdjacencyMatrix — represent a graph as an adjacency matrix

ToUnorderedPairs  ▪  FromOrderedPairs  ▪  FromUnorderedPairs

FromAdjacencyLists  ▪  FromAdjacencyMatrix  ▪  IncidenceMatrix

SymmetricQ — test if a square matrix represents a symmetric relation

EquivalenceRelationQ — test if a matrix defines an equivalence relation

AntiSymmetricQ  ▪  EquivalenceClasses  ▪  Equivalences

Displaying Graphs »

ShowGraph — display a graph

ShowGraphArray — display several graphs

GraphOptions  ▪  ShowLabeledGraph  ▪  ...

Constructing Graphs »

MakeGraph — construct a graph using a binary predicate

RandomGraph — generate a random graph

GraphUnion — construct the union of two graphs

LineGraph  ▪  AddEdges  ▪  MakeUndirected  ▪  PermuteSubgraph  ▪  ...

SetEdgeWeights — assign weights to edges

SetVertexWeights — assign weights to vertices

GetEdgeWeights  ▪  GetVertexWeights  ▪  GetEdgeLabels  ▪  GetVertexLabels

CostOfPath  ▪  DilateVertices  ▪  WeightingFunction  ▪  WeightRange  ▪  ...

Graph Input and Output

ReadGraph — read graph specification from a file

WriteGraph — write graph specification into a file

Built-in Graphs »

Cycle — a circular chain of edges

GridGraph — graph with nodes on a grid

FiniteGraphs — list of all built-in finite parameterless graphs

Wheel  ▪  Hypercube  ▪  Harary  ▪  ...