A generalized simplicial model and its application

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.