Identifying an influential spreader from a single seed in complex networks via a message-passing approach

TL;DR

This paper introduces a message-passing analytical method to accurately identify influential spreaders in complex networks by predicting epidemic outbreak sizes from single seeds.

Contribution

It develops a novel message-passing theory for calculating epidemic sizes from single seeds, improving influence ranking accuracy in complex networks.

Findings

The size of epidemic outbreaks is largely independent of seed location once an outbreak occurs.

The probability of an epidemic outbreak strongly depends on seed placement.

The approach is adaptable to weighted networks.

Abstract

Identifying the most influential spreaders is one of outstanding problems in physics of complex systems. So far, many approaches have attempted to rank the influence of nodes but there is still the lack of accuracy to single out influential spreaders. Here, we directly tackle the problem of finding important spreaders by solving analytically the expected size of epidemic outbreaks when spreading originates from a single seed. We derive and validate a theory for calculating the size of epidemic outbreaks with a single seed using a message-passing approach. In addition, we find that the probability to occur epidemic outbreaks is highly dependent on the location of the seed but the size of epidemic outbreaks once it occurs is insensitive to the seed. We also show that our approach can be successfully adapted into weighted networks.