Influence maximization in complex networks through optimal percolation

TL;DR

This paper introduces a novel method to identify the minimal set of influential nodes in complex networks by mapping the problem onto optimal percolation, revealing that influential nodes include many weakly-connected, low-degree nodes overlooked by traditional heuristics.

Contribution

The study presents a new theoretical framework for optimal influencer identification using a many-body system approach based on the non-backtracking matrix, surpassing heuristic methods.

Findings

Optimal influencers are significantly fewer than those predicted by heuristics.

Many weakly-connected low-degree nodes are identified as influential.

The method uncovers hierarchical structures of influencers overlooked by traditional approaches.

Abstract

The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network [1]; or, if immunized, would prevent the diffusion of a large scale epidemic [2,3]. Localizing this optimal, i.e. minimal, set of structural nodes, called influencers, is one of the most important problems in network science [4,5]. Despite the vast use of heuristic strategies to identify influential spreaders [6-14], the problem remains unsolved. Here, we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix [15] of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly-connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. Eventually, the present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase [16].