Network Mapping by Replaying Hyperbolic Growth

TL;DR

HyperMap is a new, simple method for mapping real networks into hyperbolic space, enabling community detection, link prediction, and efficient routing, with high accuracy and low computational complexity.

Contribution

The paper introduces HyperMap, a novel approach that replays network growth to infer hyperbolic coordinates, improving network analysis and prediction tasks.

Findings

Identifies communities within the AS Internet network.

Predicts missing links with high precision.

Achieves highly navigable hyperbolic maps for routing.

Abstract

Recent years have shown a promising progress in understanding geometric underpinnings behind the structure, function, and dynamics of many complex networks in nature and society. However these promises cannot be readily fulfilled and lead to important practical applications, without a simple, reliable, and fast network mapping method to infer the latent geometric coordinates of nodes in a real network. Here we present HyperMap, a simple method to map a given real network to its hyperbolic space. The method utilizes a recent geometric theory of complex networks modeled as random geometric graphs in hyperbolic spaces. The method replays the network's geometric growth, estimating at each time step the hyperbolic coordinates of new nodes in a growing network by maximizing the likelihood of the network snapshot in the model. We apply HyperMap to the AS Internet, and find that: 1) the method produces meaningful results, identifying soft communities of ASs belonging to the same geographic region; 2) the method has a remarkable predictive power: using the resulting map, we can predict missing links in the Internet with high precision, outperforming popular existing methods; and 3) the resulting map is highly navigable, meaning that a vast majority of greedy geometric routing paths are successful and low-stretch. Even though the method is not without limitations, and is open for improvement, it occupies a unique attractive position in the space of trade-offs between simplicity, accuracy, and computational complexity.