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Proximity networks are time-varying graphs representing the closeness amonghumans moving in a physical space. Their properties have been extensivelystudied in the past decade as they critically affect the behavior of spreadingphenomena and the performance of routing algorithms. Yet, the mechanismsresponsible for their observed characteristics remain elusive. Here, we showthat many of the observed properties of proximity networks emerge naturally andsimultaneously in a simple latent space network model, calleddynamic-$\mathbb{S}^{1}$. The dynamic-$\mathbb{S}^{1}$ does not model nodemobility directly, but captures the connectivity in each snapshot---eachsnapshot in the model is a realization of the $\mathbb{S}^{1}$ model oftraditional complex networks, which is isomorphic to hyperbolic geometricgraphs. By forgoing the motion component the model facilitates mathematicalanalysis, allowing us to prove the contact, inter-contact and weightdistributions. We show that these distributions are power laws in thethermodynamic limit with exponents lying within the ranges observed in realsystems. Interestingly, we find that network temperature plays a central rolein network dynamics, dictating the exponents of these distributions, thetime-aggregated agent degrees, and the formation of unique and recurrentcomponents. Further, we show that paradigmatic epidemic and rumor spreadingprocesses perform similarly in real and modeled networks. Thedynamic-$\mathbb{S}^{1}$ or extensions of it may apply to other types oftime-varying networks and constitute the basis of maximum likelihood estimationmethods that infer the node coordinates and their evolution in the latentspaces of real systems.

Latent geometry and dynamics of proximity networks