Abstract

BOAVENTURA-NETTO, Paulo Oswaldo. Ranking graph edges by the weight of their spanning arborescences or trees. Pesqui. Oper. [online]. 2008, vol.28, n.1, pp. 59-73. ISSN 0101-7438.  http://dx.doi.org/10.1590/S0101-74382008000100004.

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.

Keywords : graphs; matrix-tree theorem; vulnerability.