Empirical study on clique-degree distribution of networks

The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. We investigate the distribution of clique degrees, which are an extension of degree and can be used to measure the density of cliques in networks. Empirical studies indicate the extensive existence of power-law clique-degree distributions in various real networks, and the power-law exponent decreases with an increase of clique size.