Discrete Hyperbolic Random Graph Model

TL;DR

This paper introduces a discrete variant of the hyperbolic random graph model that simplifies analysis and computation, demonstrated through experiments on real and simulated networks.

Contribution

The paper proposes a discrete hyperbolic random graph model using triangulation, making the model more accessible and efficient for practical network analysis.

Findings

DHRG simplifies working with hyperbolic random graphs.

Experimental results show DHRG's effectiveness on real and simulated networks.

DHRG offers computational advantages over traditional HRG models.

Abstract

The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and conceptually challenging because of the nature of the distances in the hyperbolic plane. In this paper, we propose a discrete variant of the HRG model where nodes are mapped to the vertices of a triangulation; our algorithms allow us to work with this model in a simple yet efficient way. We present experimental results conducted on networks, both real-world and simulated, to evaluate the practical benefits of DHRG in comparison to the HRG model.