Centrality Ranking via Topologically Biased Random Walks in Multiplex Networks

Characterizing the statistically significant centrality of nodes is one of the main objectives of multiplex networks. However, current centrality rankings concentrate only on either the topological structure of the network or diffusion processes based on random walks. A pressing challenge is how to measure centralities of nodes in multiplex networks, depending both on network topology and on diffusion processes (the type of biases in the walks). 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 to which extent 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.