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A vertex labelling of a graph G is a partial map f from the vertex-set
V of G into a set L.
An edge labelling of a graph G is a partial map f from the edge-set
E of G into a set L.
A labelled graph is built by assigning labels successively to vertices or
edges after the (unlabelled) graph has been constructed.
Similarly, a capacitated graph G is a partial map from its
edge-set into Z^ +, and a weighted graph G is a partial map from
its edge-set into R, R any ring with a total order.
Those two last features are particularly convenient
when running shortest-paths and flow algorithms.
Edge capacities and edge weights are assigned to edges
once the graph has been constructed.
Any graph edge may carry a label, together with a capacity and/or a
weight.
All the functions for decorating graph vertices and edges
are fully documented in Section Vertex and Edge Decorations in
Chapter MULTIGRAPHS.
A few examples are also given there.
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