Novel Multiplex PageRank in Multilayer Networks

Multilayer networks are described as complex networks in which each node is related to all other nodes in distinct layers. These layers form a class of cooperating and interacting networks. Examples of such multilayer networks are transport networks, where people can move from one city to another through various modes of transportation. The ranking of nodes in multilayer networks is one of the most challenging and demanding tasks on complex networks. Since pairs of nodes are related through various types of links in multilayers, the ranking of nodes should inevitably reveal the weights of nodes in all corresponding layers. In this paper, we exploit the concept of populations' random migration in a multiplex transport network to propose a new Multiplex PageRank centrality measure, where the effects of influence and feedback between networks on the centrality of nodes are directly considered. We apply the proposed measure to an artificial duplex network. Findings indicate that considering the network with multilayers helps uncover the rankings of nodes, which are different from the rankings in a monotonous network. Moreover, the Multiplex PageRank centrality measure of dynamical network models is discussed for further practical application and applied to an urban transport network. The results demonstrate the effectiveness of our measure in the dynamical network.