Self-similar scaling of higher-order interactions in complex networks

Abstract Self-similarity of complex networks has been exhaustively explored but only concentrating on pairwise interactions between nodes. We restudy self-similar characteristics of networks from algebraic topological perspective. By virtue of a box covering technique, we generate consecutive renormalized networks with respect to different length scales. Interestingly, we find that the number of a specific order of clique in the renormalized networks presents a clearly scaling behavior. Moreover, we show that the growth pattern of cliques is likely to follow a universal principle for seemingly different kinds of real networks. Our work, for the first time, reveals the role of higher-order interactions in shaping self-similarity of complex networks.