Structure of growing complex networks coupling with the friendship and contact relations

Understanding the structure and evolution of the social networks is a significant task. In this paper, we proposed a new evolving social networks model coupling the friendship networks and contact networks simultaneously. The mechanisms of growth and preferential attachment, random contact and disconnect, friendship decay and connection, acquaint by accident are involved. And the probabilities for a newly arrived node establishing connections to the existing vertices in each of the layers of the coupled social networks is set as a function of degrees of which at all layers. We establish and analyze the men-field model based on the evolving processes. Then the degree distributions on each of the layers are explored utilizing the mean-field model. Furthermore, we analyze and compare the degree distributions, the assortative or disassortative properties and the clustering coefficients between the two layers of the generate network by random simulations.