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Labeled multigraph

A labeled multigraph G is a multigraph with labeled nodes and edges. Formally it is a 8-tuple G=(\Sigma_V, \Sigma_E, V, E, s, t, \ell_V, \ell_E) where

  • ΣV and ΣE are finite alphabetes of the available node and edge labels,
  • V and E are disjoint sets of nodes and edges,
  • s\colon E\rightarrow\ V and t\colon E\rightarrow\ V are two maps indicating the source and target node of an edge,
  • \ell_V\colon V\rightarrow\Sigma_V and \ell_E\colon E\rightarrow\Sigma_E are two maps describing the labeling of the nodes and edges.

As a multigraph is a graph with multiple edges, i.e. edges with the same source and target node, a labeled multigraph is a labeled graph with multiple labeled edges, i.e. edges with the same source and target node and the same edge label \xi\in\Sigma_E.

10-26-2009 08:16:03
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