Latent Geometry of Human Proximity Networks

Abstract

Understanding the dynamics of human contact and movement patterns in a physical space is crucial to better understand the spread of contagious diseases, information transfer from person to person, social behavior and influence. To this end, in the last 15 years temporal networks known as human proximity networks have been captured in different settings and have been extensively studied. These networks are characterized by similar structural and dynamical properties regardless of the setting. Many of these properties are well understood and can be reproduced with simple models. However, when we examine complex social group dynamics, such as the observed recurrent formation of groups (components) that consists of the same people, simple descriptions have been elusive. In this thesis, we elucidate the emergence of the observed properties of real human proximity networks and their complex group dynamics through geometric approaches. In the first part of this thesis, we explore the human movement patterns responsible for the emergence of the main properties of the networks but in particular the formation of recurrent components. We propose a model of mobile agents, where agents reside in a hidden metric similarity space. In this space the distances between the agents abstract their similarities and these similarities act as forces that direct their motion towards each other in the physical space, and determine the duration of their interactions. We show that this force-directed motion model reproduces the main properties of human proximity networks and simultaneously forms the elusive recurrent components observed in reality. Interestingly, results with this model point to a connection with the popular S1 model of traditional (non-mobile) complex networks, which is isomorphic to random hyperbolic graphs. In the second part of this thesis, we explore this connection and propose a minimal latent space model which reproduces all the main properties of human proximity networks as well as the formation of recurrent components. The simplicity of the model facilitates its mathematical analysis, allowing us to prove three important properties of the generated networks. These findings lead to the third part of this thesis, where we address the problem of mapping real human proximity networks into hyperbolic spaces. We show that this embedding process can be done using methods developed for traditional complex networks based on the S1 model. We justify the compatibility theoretically and experimentally. We produce hyperbolic maps of six different real systems, which can be used to identify communities, facilitate greedy routing, and predict future links with significant precision. Further, we show that the time when nodes become infected are positively correlated with their hyperbolic distance from the source of the infection in epidemic spreading simulations on the temporal network.