Identifying critical higher-order interactions in complex networks

TL;DR

This paper introduces a novel method to identify critical higher-order interactions in complex networks, redefining centrality measures with new Laplacians and validating their effectiveness through SIR simulations.

Contribution

The paper proposes two new Laplacians to redefine centrality measures for higher-order interactions, advancing the analysis of complex network dynamics.

Findings

Proposed Laplacians effectively identify critical higher-order interactions.

Redefined centrality measures outperform traditional methods in simulations.

Experimental results confirm the method's promise in network analysis.

Abstract

Information diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, cascading failures in power grids. The critical interactions in networks are the ones that play critical roles in information diffusion and primarily affect network structure and functions. Besides, interactions can occur between not only two nodes as pairwise interactions, i.e., edges, but also three or more nodes, described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions. We propose two new Laplacians that allow redefining classical graph centrality measures for higher-order interactions. We then compare the redefined centrality measures using the Susceptible-Infected-Recovered (SIR) simulation model. Experimental results suggest that the proposed method is promising in identifying critical higher-order interactions.