Vital node identification in hypergraphs via gravity model

TL;DR

This paper introduces a gravity model-based centrality method for hypergraphs, effectively identifying vital nodes that influence spreading and connectivity, with a balance between accuracy and computational efficiency.

Contribution

The paper proposes a novel gravity model-based centrality measure for hypergraphs and introduces evaluation metrics tailored for higher-order structures.

Findings

HGC effectively identifies nodes with high spreading influence.

LHGC balances accuracy and computational complexity.

Methods outperform existing centrality measures in hypergraph connectivity.

Abstract

Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality problem has attracted abundant attention due to the challenge of how to utilize the higher-order structure for the definition of centrality metrics. In this paper, we propose a new centrality method (HGC) on the basis of the gravity model as well as a semi-local HGC (LHGC) which can achieve a balance between accuracy and computational complexity. Meanwhile, two comprehensive evaluation metrics, i.e., a complex contagion model in hypergraphs that mimics the group influence during the spreading process and network s-efficiency based on the higher-order distance between nodes, are first proposed to evaluate the effectiveness of our methods. The results show that our methods can filter out nodes that have fast spreading ability and are vital in terms of hypergraph connectivity.