Topologically biased random walk for diffusions on multiplex networks

Abstract

Random walks constitute a basic mechanism for diffusion processes occurring on multiplex networks composed by different layers describing interactions of different nature. However, existing random walk diffusions focus only on network topology, leading to randomly traverse both intralayer and interlayer edges with certain equal probability. In order to efficiently explore diffusions on multiplex networks, topologically biased random walks whose movement is forcedly biased toward certain topological properties of a neighboring node are introduced to such systems, depending both upon multiplex topology and upon diffusion processes (the class of bias in the walker). Here, we introduce topologically biased random walks on multiplex networks and derive analytical expressions for their long-term diffusion properties such as entropy rate and stationary probability distribution. In particular, according to the dependence of the biased function's parameters on the layer number, we propose topologically biased additive, multiplicative and multiplex random walks. Then, we study the impact of different topologies of synthetic multiplex networks on the steady-state diffusion behaviors of these walks and find that interlayer coupling strength, edge overlapping, the sign and presence of interlayer degree–degree correlations and the layer number capture the extent to which the diffusions on a multiplex network are efficiently explored by a biased walk. Experimentally we conduct diffusion processes on four real-world multiplex networks. Our results show that a better trade-off between efficient diffusion exploration and homogeneity sampling of network nodes by opportunely tuning the biased exponents toward intrinsically multiplex nodes.