Utility of algebraic connectivity metric in topology design of survivable networks

Abstract

In studies of survivable networks, it is important to be able to differentiate network topologies by means of a robust numerical measure that indicates the levels of immunity of these topologies to failures of their nodes and links. Ideally, such a measure should be sensitive to the existence of nodes or links which are more important than others, for example, if their failures cause the network's disintegration. In this paper, we suggest using an algebraic connectivity metric, adopted from spectral graph theory, namely the 2nd smallest eigenvalue of the Laplacian matrix of the network topology, instead of the average nodal degree that is usually used to characterize network connectivity in studies of the spare capacity allocation problem. Extensive simulation studies confirm that this metric is a more informative and more accurate parameter than the average nodal degree for characterizing network topologies in survivability studies.