Locating Sources in Multiplex Networks for Linear Diffusion Systems

Accurately locating sources with limited resources plays an important role in suppressing and even predicting the spread of harmful information. Due to the existence of the coupling between layers, compared with simplex networks, many studies have revealed that multiplex networks present many interesting phenomena. However, almost all the works involved in source(s) localization concentrate on simplex networks, while it is unclear how the coupling strength between layers of a multiplex network affects source(s) localization. Here we focus on a linear diffusion process and propose a general framework of multiple sources localization in multiplex networks with minimum measurements by combining the observability theory and compressed sensing theory. One surprise finding is that, for undirected two-layer networks with fully coupling between layers, the messengers placed at the same layer is sufficient to accurately locate all the sources. Different from simplex networks, the diffusion coefficients of linear diffusion process in multiplex networks can affect the minimum number of messengers. Simulation results from various network structures show that the minimum number of messengers is fewer when the coupling strength between layers is higher. Besides, we find the larger the network size the fewer measurements are required for sources localization. We further provide simulations from synthetic networks and one real network demonstrates our framework of sources localization is robust against small amount of data, noise and the coupling strength between layers.