Centrality ranking in multiplex networks using topologically biased random walks

Characterizing the statistically significant centrality of nodes is one of the main goals of multiplex networks. However, current centrality measures for node rankings focus only on either random walks or on the topological structure of the network. A pressing challenge is how to measure centrality of nodes in multiplex networks, depending both on network topology and on the biased types of random walks, such as the biased walks dealing with the properties of each node separately at each layer, or the biased walks considering instead one or even more intrinsically multiplex properties of the arrival node. In the paper, considering these two aspects, we propose a mathematical framework based on topologically biased random walk, called topologically biased multiplex PageRank, which allows to calculate centrality and accordingly rank nodes in multiplex networks. In particular, depending on the nature of biases and the interaction of nodes between different layers, we distinguish additive, multiplicative and combined cases of topologically biased multiplex PageRank. Each case by tuning the bias parameters reflects how the centrality ranking of a node in one layer affects the ranking its replica can gain in the other layers, and captures the extent to which the walkers preferentially visit hubs or poorly connected nodes. Experiments on two real-world multiplex networks show that the topologically biased multiplex PageRank outperforms both its corresponding unbiased case and the current ranking methods, and it can efficiently capture the significantly top-ranked nodes in multiplex networks by means of a proper tuning of the biases in the walks.