Hyperbolic Mapping of Human Proximity Networks

TL;DR

This paper demonstrates that human proximity networks, despite their sparsity and temporal nature, can be effectively embedded into hyperbolic space over time, enabling insights into community detection, routing, and epidemic prediction.

Contribution

It introduces a method to embed temporal human proximity networks into hyperbolic space, bridging a gap between static network embedding techniques and dynamic human contact data.

Findings

Hyperbolic maps reveal community structures in proximity networks.

Hyperbolic embedding improves greedy routing efficiency.

Distances in hyperbolic space correlate with epidemic spread timing.

Abstract

Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases and information among humans. Here we address the problem of mapping human proximity networks into hyperbolic spaces. Each snapshot of these networks is often very sparse, consisting of a small number of interacting (i.e., non-zero degree) nodes. Yet, we show that the time-aggregated representation of such systems over sufficiently large periods can be meaningfully embedded into the hyperbolic space, using methods developed for traditional (non-mobile) complex networks. We justify this compatibility theoretically and validate it experimentally. We produce hyperbolic maps of six different real systems, and show that the maps can be used to identify communities, facilitate efficient greedy routing on the temporal network, and predict future links with significant precision. Further, we show that epidemic arrival times are positively correlated with the hyperbolic distance from the infection sources in the maps. Thus, hyperbolic embedding could also provide a new perspective for understanding and predicting the behavior of epidemic spreading in human proximity systems.