Bond percolation in clustered multilayer networks

In today´s world, individuals interact with each other in more complicated patterns than ever. Some individuals engage through online social networks (e.g., Facebook, Twitter), while some communicate only through conventional ways (e.g., face-to-face). Therefore, understanding the dynamics of information propagation calls for a multi-layer network model where an online social network is conjoined with a physical network. Here, we study information diffusion in a clustered multi-layer network model, where all constituent layers are random networks with high clustering. We assume that information propagates according to the SIR model and with different information transmissibility across the networks. Taking advantage of the isomorphism between bond percolation and information propagation processes, we give results for the conditions, probability, and size of information epidemics. We show that increasing the level of clustering in either one of the layers increases the epidemic threshold and decreases the final epidemic size.