Leveraging percolation theory to single out influential spreaders in networks

TL;DR

This paper demonstrates that Non-Backtracking centrality is an optimal and reliable metric for identifying influential spreaders in complex networks, especially at criticality, using percolation theory and extensive simulations.

Contribution

It provides an exact solution for identifying influential spreaders in the SIR model at criticality, establishing Non-Backtracking centrality as the optimal criterion.

Findings

Non-Backtracking centrality accurately predicts influential spreaders at criticality.

The method is effective on both synthetic and real-world networks.

Non-Backtracking centrality remains reliable even in noncritical and non-spatial networks.

Abstract

Among the consequences of the disordered interaction topology underlying many social, techno- logical and biological systems, a particularly important one is that some nodes, just because of their position in the network, may have a disproportionate effect on dynamical processes mediated by the complex interaction pattern. For example, the early adoption by an opinion leader in a social network may change the fate of a commercial product, or just a few super-spreaders may determine the virality of a meme in social media. Despite many recent efforts, the formulation of an accurate method to optimally identify influential nodes in complex network topologies remains an unsolved challenge. Here, we present the exact solution of the problem for the specific, but highly relevant, case of the Susceptible-Infected-Removed (SIR) model for epidemic spreading at criticality. By exploiting the mapping between bond percolation and the static properties of SIR, we prove that the recently introduced Non-Backtracking centrality is the optimal criterion for the identification of influential spreaders in locally tree-like networks at criticality. By means of simulations on synthetic networks and on a very extensive set of real-world networks, we show that the Non-Backtracking centrality is a highly reliable metric to identify top influential spreaders also in generic graphs not embedded in space, and for noncritical spreading.