Hybrid evolving clique-networks and their communicability

•We propose a hybrid clique network model to mimic the behaviors of real-world hierarchical networks.•An inhomogeneity parameter is introduced to tune the fraction of the inhomogeneous parts of the networks.•The numerical investigations on the properties and communicability of this network are presented.

Aiming to understand real-world hierarchical networks whose degree distributions are neither power law nor exponential, we construct a hybrid clique network that includes both homogeneous and inhomogeneous parts, and introduce an inhomogeneity parameter to tune the ratio between the homogeneous part and the inhomogeneous one. We perform Monte-Carlo simulations to study various properties of such a network, including the degree distribution, the average shortest-path-length, the clustering coefficient, the clustering spectrum, and the communicability.