GraphDistance

The length of a shortest u to v path, respecting edge direction.

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GraphDistance(g, u, v)the number of edges on a shortest

u \to v

path, or

+\infty

v

is unreachable from

u

Typed signatures

Type	Package	Applies
`(value, any, any) -> value`	`combinatorics`	always

Domain: Collections

Details

Weighted (g carries EdgeWeight -> {…}): the SUM of edge weights along the cheapest path (Dijkstra), not an edge count — read numerically, so an exact weight (a fraction, say) comes back as a float, not kept exact. Requires every weight non-negative; a negative one leaves the call unevaluated (see FindShortestPath's own note).

Examples

1 more kept as data, checked against the oracles

Basic #

\mathrm{GraphDistance}(\mathrm{PathGraph}(5), 1, 5)

Out

4

No directed path back, so the distance is infinite

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

Out

∞

With EdgeWeight given, the distance is the summed weight along the path (5 + 7), not the 2-edge hop count

\mathrm{GraphDistance}(\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)), 1, 3)

Out

12

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