Finding the infection sources in a network when we only know the network topology and infected nodes, but not the rates of infection, is a challenging combinatorial problem, and it is even more difficult in practice where the underlying infection spreading model is usually unknown a priori. In this paper, we are interested in finding a source estimator that is applicable to various spreading models, including the susceptible-infected (SI), susceptible-infected-recovered (SIR), susceptible-infected-recovered-infected (SIRI), and susceptible- infected-susceptible (SIS) models. We show that under the SI, SIR, and SIRI spreading models and with mild technical assumptions, the Jordan center is the infection source associated with the most likely infection path in a tree network with a single infection source. This conclusion applies for a wide range of spreading parameters, while it holds for regular trees under the SIS model with homogeneous infection and recovery rates. Since the Jordan center does not depend on the infection, recovery, and reinfection rates, it can be regarded as a universal source estimator. We also consider the case where there are k 1 infection sources, generalize the Jordan center definition to a k-Jordan center set, and show that this is an optimal infection source set estimator in a tree network for the SI model. Simulation results on various general synthetic networks and real-world networks suggest that Jordan center-based estimators consistently outperform the betweenness, closeness, distance, degree, eigenvector, and pagerank centrality-based heuristics, even if the network is not a tree.

The goal of a rumor source node in a social network is to spread its rumor to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have accepted the rumor (which are called infected nodes). We model the rumor spreading and source identification problem as a strategic game, where the rumor source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that probes every node within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the rumor source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which the Nash equilibria of the strategic game exist. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.

We consider the problem of identifying an infection source based only on an observed set of infected nodes in a network, assuming that the infection process follows a Susceptible-Infected-Susceptible (SIS) model. We derive an estimator based on estimating the most likely infection source associated with the most likely infection path. Simulation results on regular trees suggest that our estimator performs consistently better than the minimum distance centrality based heuristic.

Estimating which nodes in a network are the infection sources, including the individuals who started a rumor in a social network, the computers that introduce a virus into a computer network, or the index cases of a contagious disease, plays a critical role in identifying the influential nodes in a network, and in some applications, limiting the damage caused by the infection through timely quarantine of the sources. We consider the problem of estimating the infection sources, based only on knowledge of the underlying network connections. We derive estimators based on approximations of the infection sequences counts. We show that if there are at most two infection sources in a geometric tree, our estimator identifies these sources with probability going to one as the number of infected nodes increases. When there are more than two infection sources, we present heuristics that have quadratic complexity. We show through simulations that our proposed estimators can correctly identify the infection sources to within a few hops with high probability.