2010/11/30 by Luca Ferretti, Michele Cortelezzi, M. Cortelezzi · 40 citations
Computer Science · Mathematics · Physics and Astronomy · Social Sciences · #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Curvature #Degree (music) #Degree distribution #Distribution (mathematics) #Evolutionary Game Theory and Cooperation #Geometry #Gravitational singularity #Hyperbolic space #Mathematical analysis #Mathematics #Metric (unit) #Metric space #Physics #Preferential attachment #Space (punctuation) #Statistical physics #Stochastic processes and statistical mechanics #cond-mat.dis-nn #cond-mat.stat-mech #cs.SI #physics.soc-ph
paper · pdf · doi:10.1103/physreve.84.016103
published in Physical Review E 84(1), 016103 (American Physical Society) · 9 pages, 12 figures, revtex, final version
openalex publication_date 2011/07/08 · arxiv created 2011/11/15 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models is similar to that of the fitness model of Bianconi and Barabási, with a fitness distribution dependent on the metric and the density of nodes. We show that curvature singularities in these spaces can give rise to asymptotic Bose-Einstein condensation, but transient condensation can be observed also in smooth hyperbolic spaces with strong curvature. We provide numerical results for spaces of constant curvature (sphere, flat, and hyperbolic space) and we discuss the conditions for the breakdown of this approach and the critical points of the transition to distance-dominated attachment. Finally, we discuss the distribution of link lengths.