Small perturbation analysis of network topologies

The goal of this paper is to derive a small perturbation analysis for networks subject to random changes of a small number of edges. Small perturbation theory allows us to derive, albeit approximate, closed form expressions that make possible the theoretical statistical characterization of the network topology changes. The analysis is instrumental to formulate a graph-based optimization algorithm, which is robust against edge failures. In particular, we focus on the optimal allocation of the overall transmit powers in wireless communication networks subject to fading, aimed at minimizing the variation of the network connectivity, subject to a constraint on the overall power necessary to maintain network connectivity.