Influence Maximization on Hypergraphs via Similarity-based Diffusion

Influence maximization is an important problem in network science that aims to detect critical structures, such as nodes and interactions, with a higher influence on diffusion. It has applications in information spreading, rumor controlling, marketing, disease spreading, advertising, and more. Although the influence maximization problem in graphs has been studied ex-tensively, there are a few studies that explore critical structures in hypergraphs and these studies mostly focus on detecting influential nodes rather than higher-order interactions, i.e., hyperedges. In this paper, we study the influential hyperedge detection problem. We first design diffusion models on hypergraphs based on the similarity between hyperedges. Our claim here is that similarity between hyperedges is positively correlated with the diffusion process. To study this claim, we first calculate similarity scores between hyperedges and construct similarity-based hypergraph Laplacians. Next, we extend standard graph centrality measures for hyperedges using these Laplacians. We compare the similarity- based hypergraph Laplacians with the state-of-the-art influential hyperedge detection method using two evaluation metrics: the size of the giant component and the Susceptible-Infected-Recovered (SIR) simulation model. Our experimental results suggest that overall, similarity-based Laplacians are more effective than the state-of-the-art method in finding influential higher-order hyperedges.