GraphDistanceMatrix

All-pairs shortest-path distances of a Graph, as a matrix.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageGraphDistanceMatrix✓

GraphDistanceMatrix(g)row/column order follows VertexList(g); entry (i, j) is GraphDistance(g, v_i, v_j).

Typed signatures

Type	Package	Applies
`(value) -> list<list<real \| signed_infinity>>`	`combinatorics`	always

Domain: Collections

Details

Respects edge direction, same as GraphDistance itself -- row i is the distances FROM vertex i.
An unreachable pair reads PositiveInfinity, matching GraphDistance on a disconnected graph.
Weighted (g carries EdgeWeight): every entry is GraphDistance's own weighted (Dijkstra, summed-weight) reading, not an edge count; a negative weight leaves the WHOLE matrix unevaluated, same as GraphDistance itself.

Examples

Basic #

\mathrm{GraphDistanceMatrix}(\mathrm{CycleGraph}(3))

Out

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

\mathrm{GraphDistanceMatrix}(\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(3, 4)\bigr\rbrack))

Out

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

With EdgeWeight given, entry (1, 3) is the summed weight 5 + 7, not the 2-edge hop count

\mathrm{GraphDistanceMatrix}(\mathrm{Graph}(\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(2, 3)\bigr\rbrack, \operatorname{KeyValuePair}(\mathrm{EdgeWeight}, \bigl\lbrack5, 7\bigr\rbrack)))

Out

\bigl\lbrack\bigl\lbrack0, 5, 12\bigr\rbrack, \bigl\lbrack5, 0, 7\bigr\rbrack, \bigl\lbrack12, 7, 0\bigr\rbrack\bigr\rbrack

About