On the universality of the Jordan center for estimating the rumor source in a social network

We consider the problem of finding the source of a rumor spreading in a social network. We assume that our knowledge of the rumor spreading is limited to the graph topology of the underlying social network and which nodes recently posted the rumor, but not the rates of rumor spreading nor the rumor spreading model. we are interested in finding a source estimator that is applicable to various spreading models, including the Susceptible-Infected (SI), Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Infected (SIRI) models. We show that under all three considered rumor spreading models and with mild technical assumptions, the Jordan center is an optimal rumor source estimator under the most likely infection path criterion. This conclusion applies for a wide range of spreading parameters where nodes may have different infection, recovery and reinfection rates. Since the Jordan center does not depend on the infection, recovery and reinfection rates, it can be regarded as a universal source estimator. Simulation results on various general synthetic networks and real world networks suggest that the Jordan center consistently outperform the distance, closeness, and betweenness centrality based heuristics, even if the network is not a tree.