A generalized simplicial model and its application

TL;DR

This paper introduces a framework to quantify the impact of higher-order structures like 2-simplices on network functions, demonstrating how controlling these structures influences dynamics such as spreading, control, robustness, and community detection.

Contribution

It proposes a simplicial model that regulates higher-order structures while preserving degree sequences, enabling analysis of their effects on network functions.

Findings

Regulating 2-simplices significantly affects network performance.

The algorithm indirectly controls higher-order simplexes beyond 2-order.

The framework links micro-level structures to global network functions effectively.

Abstract

Higher-order structures, consisting of more than two individuals, provide a new perspective to reveal the missed non-trivial characteristics under pairwise networks. Prior works have researched various higher-order networks, but research for evaluating the effects of higher-order structures on network functions is still scarce. In this paper, we propose a framework to quantify the effects of higher-order structures (e.g., 2-simplex) and vital functions of complex networks by comparing the original network with its simplicial model. We provide a simplicial model that can regulate the quantity of 2-simplices and simultaneously fix the degree sequence. Although the algorithm is proposed to control the quantity of 2-simplices, results indicate it can also indirectly control simplexes more than 2-order. Experiments on spreading dynamics, pinning control, network robustness, and community detection have shown that regulating the quantity of 2-simplices changes network performance significantly. In conclusion, the proposed framework is a general and effective tool for linking higher-order structures with network functions. It can be regarded as a reference object in other applications and can deepen our understanding of the correlation between micro-level network structures and global network functions.