On the Robustness of Interconnections in Random Graphs: A Symbolic Approach
Résumé
Graphs are models of communication networks. This paper applies symbolic combinatorial techniques in order to characterize the interplay between two parameters of a random graph, namely its density (the number of edges in the graph) and its robustness to link failures. Here, robustness means multiple connectivity by short disjoint paths. We determine the expected number of ways to get from a source to a destination via two edge-disjoint paths of length $\ell$ in the classical random graph model $\G_n,p$. We then derive bounds on related threshold probabilities.