Analyse de la vulnérabilité d’un réseau via la mesure de l’entropie de Von Neumann.

Abstract

In this work, we present a new strategy for measuring the vulnerability of network connections, modeled by a graph, via the variations of the Von Neumann entropy of the density matrix associated to this graph, this one being seen as a quantum system. We show that the change of the weight of an edge impacts the resulting Von Neumann entropy, which includes not only the intensity of the perturbation induced but also a quantity related to the degrees of the nodes adjacent to the perturbed edge. An algorithm based on this strategy has been developed. The obtained results confirm the relevance of this new measure. Our algorithm highlights the discontinuities that could appear in the structure by proposing a hierarchical decomposition into subgraphs relative to the degrees of vulnerability of the edges. The obtained map guarantees a better network security.