  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.
