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Ranking graph edges by the weight of their spanning arborescences or trees

A result based on a classic theorem of graph theory is generalized for edge-valued graphs, allowing determination of the total value of the spanning arborescences with a given root and containing a given arc in a directed valued graph. A corresponding result for undirected valued graphs is also presented. In both cases, the technique allows for a ranking of the graph edges by importance under this criterion. This ranking is proposed as a tool to determine the relative importance of the edges of a graph in network vulnerability studies. Some examples of application are presented.

graphs; matrix-tree theorem; vulnerability


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