The Kronecker-clique model for higher-order clustering coefficients

Abstract We propose a Kronecker-clique model, which possesses the higher-order properties, i.e., high-order clustering coefficients, of real-world networks. The higher-order clustering coefficient is defined as the closure probability of cliques. The higher-order structure of Kronecker-clique model is formed by introducing some cliques into the stochastic Kronecker model according to the degree-dependent function. We compare the higher-order clustering coefficients of the Kronecker-clique model with those of the stochastic Kronecker model and the HyperKron model when fitting the real-world networks. The results indicate that the Kronecker-clique model performs better than the stochastic Kronecker model, the HyperKron model as well as the traditional clustered model. Moreover, we perform k -core decomposition and show that the maximum k -core of the Kronecker-clique model is closer to that of real-world networks compared with the stochastic Kronecker model.