Diffusion of Real-Time Information in Overlaying Social-Physical Networks: Network Coupling and Clique Structure

We study the diffusion behavior of real-time information in an overlaying social-physical network. Typically, real-time information is valuable only for a limited time duration and needs to be delivered before its deadline, indicating that real-time information is more likely to spread among friends within a “social proximity.” With this insight, we consider a physical information network which consists of many cliques and assume that real-time information can spread quickly within a clique. Conjoint to this physical information network, there are online social networks where the information can propagate via websites such as Facebook, twitter, Youtube, etc. Capitalizing on the theory of inhomogeneous random graph, we analytically characterize the size of information epidemic. One interesting finding is that a larger size online social network, with the same degree distribution, may not necessarily yield a larger size of information epidemic in this overlaying social-physical network. In fact, under certain conditions, the size of information epidemic could even decrease with the growing size of the online social network. This is in stark contrast to that in a single network.