Séminaire

In this talk, we consider the situation where a given graph has to be protected against communication interruption, through insurance or prevention measures. The goal of the protection buyer is to maintain good connectivity properties of the graph after a malicious attack, giving rise to a virus spread on the network. We model the epidemic spread using the standard Susceptible-Infected-Susceptible (SIS) Markov process. The connectivity of the graph is measured by a function of the average Laplacian spectrum: the second smallest eigenvalue, known as the algebraic connectivity. Using standard results on eigenvalues optimization, we recast the algebraic connectivity maximization as a semidefinite optimization problem, for which a solution exists and can be efficiently numerically computed. Our results allow to hierarchize the edges of a graph, giving more importance to some edges for which the protection demand is high, hence making optimal insurance demand directly depend on the underlying network topology. This is based on a joint work with Thierry Cohignac (Groupe CCR, Paris).

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