Complex networks on hyperbolic surfaces

2004/08/20 by Tomaso Aste, T. Aste, T. Di Matteo +3 · 2 citations
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Topological and Geometric Data Analysis #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physa.2004.08.045

published as Physica A 346 (2005) 20-26 · 8 Pages 3 Figures

arxiv created 2004/08/20 · openalex publication_date 2004/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties. This method provides a new perspective to classify network-complexity both on local and global scale. We demonstrate by means of several examples that there is a strong relation between the network properties and the embedding surface.

Citations

• Statistical mechanics of complex networks
• The structure and function of complex networks

Cited by

• Information Filtering Networks: Theoretical Foundations, Generative Methodologies, and Real-World Applications
• Geometrical structure of disordered sphere packings