On the Universality of Jordan Centers for Estimating Infection Sources in Tree Networks

TL;DR

This paper demonstrates that the Jordan center is a universal and effective estimator for infection sources across various spreading models in tree networks, and extends the concept to multiple sources, outperforming traditional centrality heuristics.

Contribution

It proves the universality of the Jordan center as a source estimator for multiple infection models in trees and generalizes it to multiple sources, with strong empirical validation.

Findings

Jordan center accurately estimates infection sources in tree networks.

The method outperforms traditional centrality heuristics in diverse networks.

The approach is effective even when the underlying spreading model is unknown.

Abstract

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.