A novel weighted evolving network model based on clique overlapping growth

A novel weighted evolving network model based on the clique overlapping growth was proposed. The model shows different network characteristics under two different selection mechanisms that are preferential selection and random selection. On the basis of mean-field theory, this model under the two different selection mechanisms was analyzed. The analytic equations of distributions of the number of cliques that a vertex joins and the vertex strength of the model were given. It is proved that both distributions follow the scale-free power-law distribution in preferential selection mechanism and the exponential distribution in random selection mechanism, respectively. The analytic expressions of exponents of corresponding distributions were obtained. The agreement between the simulations and analytical results indicates the validity of the theoretical analysis. Finally, three real transport bus networks (BTNs) of Beijing, Shanghai and Hangzhou in China were studied. By analyzing their network properties, it is discovered that these real BTNs belong to a kind of weighted evolving network model with clique overlapping growth and random selection mechanism that was proposed in this context.