A general approach of generating multiplex networks with overlapped links

There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different layers of networks, for example, in social networks where each individual node has different kinds of social ties or transportation systems where each location is connected to another location by different types of transport. Many of these multiplexes are characterized by a significant overlap of the links in different layers. However, so far the overlap of the links in different layers has been mostly neglected, despite the fact that it is an ubiquitous phenomenon in most multiplexes. In this paper we introduce a general algorithm to generate a multiplex networks with overlapped links. In this approach, we make efforts to maximize the average nodal degree of the multiplex networks. We hope the algorithm will shed light on the multiplex networks generations.