A modified algorithm of multiplex networks generation based on overlapped links

Multiplex networks, where nodes may interact through several different types of links, have been used widely to describe various complex systems. Many complex systems have an important feature that pairs of nodes may be connected by different types of links at the same time. In order to study the effect of the overlapped links systematically, in this paper I propose an algorithm to generate general multiplex networks with overlapped links. This algorithm could construct multiplex networks with arbitrary degree-degree distribution in each layer, and more importantly, could further adjust the proportion of overlapped links over a wide range. Therefore, the algorithm proposed in this paper offers an approach to construct multiplex networks into a delicate extent, which may provide a formal setting to study the topological impact of multiplex networks in a systematic manner.