EdgeMultiplicity(G, e) returns the edge multiplicity of e in G. This a nonnegative integer indicating the number of times the edge e appears in G.

EdgeMultiplicity(G) returns the edge multiplicity matrix of G. This a square matrix A where $A_{i,j}$ is the number of edges from vertex i to vertex j in the graph G.

IsMultigraph(G) returns true if G is a multigraph.

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

$\mathrm{G1}≔\mathrm{Graph}\left(5\,\mathrm{Trail}\left(1\,2\,3\,4\,3\right)\right)$

$\mathrm{G1}≔\mathrm{Graph\; 1:\; an\; undirected\; multigraph\; with\; 5\; vertices\; and\; 4\; edge(s)}$

$\mathrm{EdgeMultiplicity}\left(\mathrm{G1}\,\left\{3\,4\right\}\right)$

$2$

$\mathrm{IsMultigraph}\left(\mathrm{G1}\right)$

$\mathrm{true}$

$\mathrm{G2}≔\mathrm{Graph}\left(5\,\left\{\left\{1\,2\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{3\,5\right\}\right\}\right)$

$\mathrm{G2}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 4\; edge(s)}$

$\mathrm{EdgeMultiplicity}\left(\mathrm{G2}\,\left\{1\,2\right\}\right)$

$1$

$\mathrm{IsMultigraph}\left(\mathrm{G2}\right)$

$\mathrm{false}$

The GraphTheory[EdgeMultiplicity] and GraphTheory[IsMultigraph] commands were introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.