Rules can involve several copies of the same relation, corresponding to multiedges in a graph. A simple example is the rule:

{{x, y}} -> {{x, z}, {x, z}, {y, z}}

RulePlot[ResourceFunction[
"WolframModel"][{{x, y}} -> {{x, z}, {x, z}, {y, z}}],
VertexLabels -> Automatic, "RulePartsAspectRatio" -> 0.25]

Running this rule produces a structure with 3^{n} edges and nodes at step *n*:

ResourceFunction[
"WolframModel"][{{{x, y}} -> {{x, z}, {x, z}, {y, z}}}, {{1, 1}},
5]["StatesPlotsList", "MaxImageSize" -> 180]

Rules can both create and destroy multiedges. The rule

{{x, y}} -> {{x, z}, {z, w}, {y, z}}

RulePlot[ResourceFunction[
"WolframModel"][{{x, y}} -> {{x, z}, {y, z}, {z, w}}],
VertexLabels -> Automatic, "RulePartsAspectRatio" -> 1]

generates a multiedge after one step, but then destroys it:

ResourceFunction[
"WolframModel"][{{{x, y}} -> {{x, z}, {z, w}, {y, z}}}, {{1, 1}},
5]["StatesPlotsList", "MaxImageSize" -> 180]