AdjacencyMatrix

The vertex-by-vertex adjacency matrix of a Graph, indexed by VertexList order.

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AdjacencyMatrix(g)entry

(i, j)

is the number of edges from vertex

i

to vertex

j

— 0 or 1 for a simple graph, symmetric when every edge is undirected.

Typed signatures

Type	Package	Applies
`(value) -> list<list<integer>>`	`combinatorics`	always

Domain: Collections

Details

Returned as a plain matrix (a list of lists) rather than Wolfram's default SparseArray — a deliberate simplification here, since this library has no sparse-matrix head to return instead.

Examples

Basic #

$K_4$ 's adjacency matrix — every off-diagonal entry is 1

\mathrm{AdjacencyMatrix}(\mathrm{CompleteGraph}(4))

Out

\bigl\lbrack\bigl\lbrack0, 1, 1, 1\bigr\rbrack, \bigl\lbrack1, 0, 1, 1\bigr\rbrack, \bigl\lbrack1, 1, 0, 1\bigr\rbrack, \bigl\lbrack1, 1, 1, 0\bigr\rbrack\bigr\rbrack

A single directed edge gives an asymmetric matrix

\mathrm{AdjacencyMatrix}(\mathrm{Graph}(\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack\mathrm{DirectedEdge}(1, 2)\bigr\rbrack))

Out

\bigl\lbrack\bigl\lbrack0, 1\bigr\rbrack, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack

Properties #

\mathrm{Shape}(\mathrm{AdjacencyMatrix}(g))

Out

\mathrm{Shape}(\mathrm{AdjacencyMatrix}(g))

Possible issues #

\mathrm{AdjacencyMatrix}(\mathrm{Graph}(\bigl\lbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack))

Out

\bigl\lbrack\bigr\rbrack

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