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. In this paper, we investigate the distribution of clique-degree, which is an extension of degree and can be used to measure the density of cliques in networks. The empirical studies indicate the extensive existence of power-law clique-degree distributions in various real networks, and the power-law exponent decreases with the increasing of clique size. 
Wei-Ke Xiao, Jie Ren, Qi Feng, Zhi-Wei Song, Meng-Xiao Zhu, Hong-Feng   Yang, Hui-Yu Jin, Bing-Hong Wang, and Tao Zhou