Finding shortest and nearly shortest path nodes in large substantially incomplete networks

TL;DR

This paper reveals that shortest paths in large, incomplete networks follow latent geometric rules in hyperbolic space, enabling the identification of key nodes even with incomplete data, with applications in biology and security.

Contribution

It introduces a latent-geometric approach to find shortest and nearly shortest path nodes in large incomplete networks, leveraging hyperbolic space embeddings.

Findings

Shortest paths align along geodesics in hyperbolic space.

Latent-geometric methods identify key nodes in incomplete networks.

Applications demonstrated in cellular pathways and communication security.

Abstract

Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Unfortunately, our maps of most large networks are substantially incomplete due to either the highly dynamic nature of networks, or high cost of network measurements, or both, rendering traditional path finding methods inefficient. We find that shortest paths in large real networks, such as the network of protein-protein interactions (PPI) and the Internet at the autonomous system (AS) level, are not random but are organized according to latent-geometric rules. If nodes of these networks are mapped to points in latent hyperbolic spaces, shortest paths in them align along geodesic curves connecting endpoint nodes. We find that this alignment is sufficiently strong to allow for the identification of shortest path nodes even in the case of substantially incomplete networks. We demonstrate the utility of latent-geometric path-finding in problems of cellular pathway reconstruction and communication security.