Influence maximization based on threshold models in hypergraphs

Influence maximization problem has received significant attention in recent years due to its application in various domains, 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. First, 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 hypergraph 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 simulations 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 the HCI-TM algorithm works better for larger average hyperdegrees in Erdös-Rényi hypergraphs and smaller power-law exponents in scale-free hypergraphs.