Influence Maximization based on Threshold Model in Hypergraphs

TL;DR

This paper introduces a new framework for influence maximization in hypergraphs using a threshold model, extending message passing techniques and proposing the HCI-TM algorithm, which outperforms existing methods in simulations.

Contribution

It develops a theoretical analysis framework for collective influence in hypergraphs and proposes the HCI-TM algorithm for influence maximization.

Findings

HCI-TM outperforms competing algorithms in simulations.

HCI can predict cascading phenomena.

HCI-TM is more effective in hypergraphs with larger hyperdegrees or smaller power-law exponents.

Abstract

Influence Maximization problem has received significant attention in recent years due to its application in various do?mains such as product recommendation, public opinion dissemination, and disease propagation. This paper proposes a theoretical analysis framework for collective influence in hypergraphs, focusing on identifying a set of seeds that maximize influence in threshold models. Firstly, we extend the Message Passing method from pairwise networks to hypergraphs to accurately describe the activation process in threshold models. Then we introduce the concept of hyper?graph collective influence (HCI) to measure the influence of nodes. Subsequently, We design an algorithm, HCI-TM, to select the Influence Maximization Set, taking into account both node and hyperedge activation. Numerical simu?lations demonstrate that HCI-TM outperforms several competing algorithms in synthetic and real-world hypergraphs. Furthermore, we find that HCI can be used as a tool to predict the occurrence of cascading phenomena. Notably, we find that HCI-TM algorithm works better for larger average hyperdegrees in Erdos-R\'enyi (ER) hypergraphs and smaller power-law exponents in scale-free (SF) hypergraphs.