  Proximity networks are time-varying graphs representing the closeness among
humans moving in a physical space. Their properties have been extensively
studied in the past decade as they critically affect the behavior of spreading
phenomena and the performance of routing algorithms. Yet, the mechanisms
responsible for their observed characteristics remain elusive. Here, we show
that many of the observed properties of proximity networks emerge naturally and
simultaneously in a simple latent space network model, called
dynamic-$\mathbb{S}^{1}$. The dynamic-$\mathbb{S}^{1}$ does not model node
mobility directly, but captures the connectivity in each snapshot---each
snapshot in the model is a realization of the $\mathbb{S}^{1}$ model of
traditional complex networks, which is isomorphic to hyperbolic geometric
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. Interestingly, we find that network temperature plays a central role
in network dynamics, dictating the exponents of these distributions, the
time-aggregated agent degrees, and the formation of unique and recurrent
components. Further, we show that paradigmatic epidemic and rumor spreading
processes perform similarly in real and modeled networks. The
dynamic-$\mathbb{S}^{1}$ or extensions of it may apply to other types of
time-varying networks and constitute the basis of maximum likelihood estimation
methods that infer the node coordinates and their evolution in the latent
spaces of real systems.
