2004/11/30 by Janusz A. Hołyst, Janusz A. Holyst, Julian Sienkiewicz +3
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Complex network #Degree (music) #Discrete mathematics #Geometry #Graph #Mathematics #Node (physics) #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Random graph #Scale-free network #Scaling #Statistical physics #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.72.026108
published as Phys. Rev. E 72, 026108 (2005) · 4 pages, 3 figures, 1 table
openalex publication_date 2005/08/08 · arxiv created 2005/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Universal scaling of distances between vertices of Erdos-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k(i) and k(j) equals to (l(ij)) = A - B log(k(i)k(j)). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree (k)nn calculated for the nearest neighbors and on network clustering coefficients.