Weighted algebraic connectivity metric for non-uniform traffic in reliable network design

In network survivability design, it is important to be able to differentiate network topologies by means of a quantitative measure that would indicate different levels of robustness 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 critical than others, for example, if their failures can disconnect a network. The frequency of nodes and links being used in survivable routing, and thus their importance, can also depend on directional characteristics of non-uniform traffic demands. In this paper, we suggest to quantify network topologies with specific directional non-uniform traffic demands by a weighted algebraic connectivity metric, a generalization of algebraic connectivity metric used in the spectral graph theory, where it is defined as the 2^nd smallest eigenvalue of the Laplacian matrix of the graph. Our simulation-based studies of the spare capacity allocation problem show that this metric is a useful parameter for characterizing the impact of both the network topology and the traffic demands in network survivability studies.