Modeling human proximity networks with random hyperbolic graphs

Abstract

Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Understanding their properties is critical because they affect the behavior of disease and information spreading, as well as the formation and evolution of communities. Interestingly, a simple model of mobile agents, which assumes the agents perform random walks, reproduces a wide variety of these properties. However, until recently the mechanisms responsible for more complex social behavior remained elusive. Specifically, random walks cannot reproduce the recurrent formation of groups of the same people, which originate from human motion patterns that are far from random. We show that many of the properties of proximity networks, including the formation of recurrent groups (components), emerge naturally and simultaneously in a simple latent space model, called dynamic-S1. The dynamic-S1 does not model agent mobility, but captures their connectivity in each snapshot--each snapshot in the model is a realization of the S1 model of traditional complex networks, which is isomorphic to random hyperbolic graphs. By forgoing the motion component the model facilitates mathematical analysis, allowing us to prove the contact, inter-contact and weight distributions. We show that these distributions are power laws in the thermodynamic limit with exponents lying within the ranges observed in real systems. Furthermore, the behavior of compartmental epidemic spreading processes, such as SIS and SEIR, is remarkably similar in real and modeled networks. We have also shown that the time-aggregated representation of real human proximity networks can be meaningfully embedded into hyperbolic space, using methods developed for the S1 model. Using the resulting embeddings one can identify communities, facilitate greedy routing on the temporal network, and predict future links. Taken altogether, our results indicate that dynamic random hyperbolic graphs are adequate null models of human proximity networks.