Generating massive complex networks with hyperbolic geometry faster in practice

TL;DR

This paper introduces a significantly faster algorithm for generating large hyperbolic complex networks, enabling rapid creation of billion-edge graphs and supporting dynamic network modeling.

Contribution

The paper presents a novel, faster hyperbolic graph generator with speedup factors of 3-60 and a dynamic extension for modeling network evolution.

Findings

Achieved 3-60x speedup over previous methods

Generated 1 billion edges in under one minute

Developed a dynamic extension for network evolution

Abstract

Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. The commonly used graph-based benchmark model R-MAT has some drawbacks concerning realism and the scaling behavior of network properties. A complex network model gaining considerable popularity builds random hyperbolic graphs, generated by distributing points within a disk in the hyperbolic plane and then adding edges between points whose hyperbolic distance is below a threshold. We present in this paper a fast generation algorithm for such graphs. Our experiments show that our new generator achieves speedup factors of 3-60 over the best previous implementation. One billion edges can now be generated in under one minute on a shared-memory workstation. Furthermore, we present a dynamic extension to model gradual network change, while preserving at each step the point position probabilities.