WienerIndex returns the Wiener index of a graph G.

If G is disconnected, then WienerIndex returns infinity.

The Wiener index of a graph is the sum of the lengths of the shortest paths between all pairs of vertices in the graph.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$P≔\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{WienerIndex}\left(P\right)$

$30$

$C≔\mathrm{CycleGraph}\left(19\right)$

$C≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 19\; vertices\; and\; 19\; edge(s)}$

$\mathrm{WienerIndex}\left(C\right)$

$38$

The GraphTheory[WienerIndex] command was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.