Locating influential nodes in hypergraphs via fuzzy collective influence

TL;DR

This paper introduces fuzzy collective influence methods tailored for hypergraphs to identify influential nodes involved in complex contagion processes, outperforming traditional centrality measures in empirical tests.

Contribution

It presents a novel higher-order distance-based fuzzy centrality framework specifically designed for hypergraphs, enhancing the identification of influential nodes in complex systems.

Findings

Proposed methods outperform baseline centralities in empirical hypergraph tests.

Effective in identifying top influential nodes in higher-order interaction networks.

Framework offers new insights into influence maximization and network dismantling.

Abstract

Complex contagion phenomena, such as the spread of information or contagious diseases, often occur among the population due to higher-order interactions between individuals. Individuals who can be represented by nodes in a network may play different roles in the spreading process, and thus finding the most influential nodes in a network has become a crucial topic in network science for applications such as viral marketing, rumor suppression, and disease control. To solve the problem of identifying nodes that have high influence in a complex system, we propose a higher-order distance-based fuzzy centrality methods (HDF and EHDF) that are customized for a hypergraph which can characterize higher-order interactions between nodes via hyperedges. The methods we proposed assume that the influence of a node is reliant on the neighboring nodes with a certain higher-order distance. We compare the proposed methods with the baseline centrality methods to verify their effectiveness. Experimental results on six empirical hypergraphs show that the proposed methods could better identify influential nodes, especially showing plausible performance in finding the top influential nodes. Our proposed theoretical framework for identifying influential nodes could provide insights into how higher-order topological structure can be used for tasks such as vital node identification, influence maximization, and network dismantling.