Targeted influence maximization in complex networks

TL;DR

This paper introduces a novel theoretical framework and practical method for targeted influence maximization in complex networks, focusing on selecting optimal spreaders to influence specific target nodes while minimizing impact on others.

Contribution

It develops a message passing-based approach and a targeted collective influence metric to effectively identify influential spreaders for targeted spreading tasks.

Findings

Outperforms existing heuristic methods in synthetic and real-world networks.

Provides a new theoretical framework for targeted influence maximization.

Validates the approach with empirical results on various network types.

Abstract

Many real-world applications based on spreading processes in complex networks aim to deliver information to specific target nodes. However, it remains challenging to optimally select a set of spreaders to initiate the spreading process. In this paper, we study the targeted influence maximization problem using a susceptible-infected-recovered (SIR) model as an example. Formulated as a combinatorial optimization, the objective is to identify a given number of spreaders that can maximize the influence over target nodes while minimize the influence over non-target nodes. To find a practical solution to this optimization problem, we develop a theoretical framework based on a message passing process and perform a stability analysis on the equilibrium solution using non-backtracking (NB) matrices. We propose that the spreaders can be selected by imposing optimal perturbation on the equilibrium solution for the subgraph consisting of the target nodes and their multi-step nearest neighbors while avoiding such perturbation on the complement graph that excludes target nodes from the original network. We further introduce a metric, termed targeted collective influence, for each node to identify influential spreaders for targeted spreading processes. The proposed method, validated in both synthetic and real-world networks, outperforms other competing heuristic approaches. Our results provide a framework for analyzing the targeted influence maximization problem and a practical method to identify spreaders in real-world applications.