Identification of Missing Links Using Susceptible-Infected-Susceptible Spreading Traces

The study of Susceptible-Infected-Susceptible (SIS) spreading on complex networks has stressed the role of the network topology which is often not entirely available in practical cases. This paper addresses the problem of inferring the network links from observed SIS temporal traces. In this paper, we first derive the likelihood of an observed SIS temporal traces and then we show how Bayesian inference can be applied to infer the probability that the uncertain links exist. Moreover, formulating this network reconstruction problem as a Bayesian problem enables us to take advantage of the numerical methods already developed for Bayesian inference. In order to demonstrate the capability of the proposed approach, we performed several simulations where we were able to reconstruct the network from the SIS traces.