The interaction between multiplex community networks.

Multiplex community networks, consisting of several different types of simplex networks and interconnected among them, are ubiquitous in the real world. In this paper, we carry out a quantitative discussion on the interaction among these diverse simplex networks. First, we define two measures, mutual-path-strength and proximity-node-density, based on twoplex community networks and then propose an impact-strength-index (ISI) to describe the influence of a simplex network on the other one. Finally, we apply the measure ISI to make an explanation for the challenge system of social relations from the viewpoint of network theory. Numerical simulations show that the measure ISI can describe the interaction between multiplex community networks perfectly.