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.