quality:corruption
Labeling

Multigraphs and multidigraphs also support the notion of graph labeling, in a similar way. However there is no unity in terminology in this case.

The definitions of labeled multigraphs and labeled multidigraphs are similar, and we define only the latter ones here.

Definition 1: A labeled multidigraph is a labeled graph with labeled arcs.

Formally: A labeled multidigraph G is a multigraph with labeled vertices and arcs. Formally it is an 8-tuple G = (Σ V, Σ A, V, A, s, t, ℓ V, ℓ A) {\displaystyle G=(\Sigma _{V},\Sigma _{A},V,A,s,t,\ell _{V},\ell _{A})} where

Definition 2: A labeled multidigraph is a labeled graph with multiple labeled arcs, i.e. arcs with the same end vertices and the same arc label (note that this notion of a labeled graph is different from the notion given by the article graph labeling).