Graph Construction and Representations

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 ▪ ...

• Graph Algorithms
• Cycles and Connectivity