directed = true or false

Specifies whether the returned graph should be directed or undirected. By default, the resulting graph is undirected when the relation f is symmetric, and directed otherwise.

selfloops = true or false

Specifies whether the returned graph should contain a self-loop on vertex u when f(u,u) is true. The default is false.

RelationGraph(V,f) constructs a graph on the given vertex list in which edges exist in the graph when a Boolean predicate f is true.

If V is a list of integers, strings or symbols, then a graph is built with vertex set V in which there is an edge from a to b whenever f(a,b) returns true.

If V is a list consisting of two lists V1 and V2 of integers, strings or symbols, then a graph is built whose vertex set is the the union of V1 and V2 in which there is an edge from a in V1 to b in V2 whenever f(a,b) returns true. If V1 and V2 are disjoint, this graph is bipartite.

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

$\mathrm{G1}≔\mathrm{RelationGraph}\left(\left[\mathrm{seq}\left(1..25\right)\right]\,\mathrm{NumberTheory}:-\mathrm{AreCoprime}\right)$

$\mathrm{G1}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 25\; vertices\; and\; 199\; edge(s)}$

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

$199$

$\mathrm{DivisibleBy}≔\left(p\,q\right)\mapsto \mathrm{evalb}\left(\mathrm{irem}\left(p\,q\right)=0\right)\:$

$\mathrm{DivisibleBy}\left(4\,2\right)$

$\mathrm{true}$

$\mathrm{DivisibleBy}\left(5\,3\right)$

$\mathrm{false}$

$\mathrm{G2}≔\mathrm{RelationGraph}\left(\left[\mathrm{seq}\left(1..20\right)\right]\,\mathrm{DivisibleBy}\right)$

$\mathrm{G2}≔\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 20\; vertices\; and\; 46\; arc(s)}$

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

$46$

$\mathrm{G3}≔\mathrm{RelationGraph}\left(\left[\left[1859\,5832\,6561\,8192\,8575\right]\,\left[2\,3\,5\right]\right]\,\mathrm{DivisibleBy}\right)$

$\mathrm{G3}≔\mathrm{Graph\; 3:\; a\; directed\; graph\; with\; 8\; vertices\; and\; 5\; arc(s)}$

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

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