Characterizing the analogy between hyperbolic embedding and community structure of complex networks

TL;DR

This paper reveals that community structures in networks can serve as a simplified representation of hyperbolic embeddings, enabling new insights into network robustness and navigation without complex embedding procedures.

Contribution

It demonstrates a novel analogy between hyperbolic embedding and community structure, and introduces practical methods for network robustness and routing based on community analysis.

Findings

Community structure correlates with hyperbolic embedding.

Robustness of multiplex networks can be tuned via community correlation.

Efficient greedy routing protocol based on community structure.

Abstract

We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We take advantage of the analogy for reinterpreting results originally obtained through network hyperbolic embedding in terms of community structure only. First, we show that the robustness of a multiplex network can be controlled by tuning the correlation between the community structures across different layers. Second, we deploy an efficient greedy protocol for network navigability that makes use of routing tables based on community structure.