Structural transitions in scale-free networks

2002/08/28 by Gábor Szabó, Gabor Szabo, Mikko J. Alava +3 · 6 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Bioinformatics and Genomic Networks #Cartography #Complex Network Analysis Techniques #Complex network #Computer science #Geography #Opinion Dynamics and Social Influence #Scale (ratio) #Scale-free network #World Wide Web #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.67.056102

4 pages, 3 figures, RevTex format

arxiv created 2002/08/28 · openalex publication_date 2003/05/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Real growing networks such as the World Wide Web or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabási-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean-field rate equation for clustering. This is solved for a specific case with the result C(k) approximately 1/k for the clustering of a node of degree k. This mean-field exponent agrees with simulations, and reproduces the clustering of many real networks.

Citations

• Dynamical and Correlation Properties of the Internet
• Emergence of scaling in random networks
• Hierarchical organization in complex networks
• Epidemic Threshold in Structured Scale-Free Networks
• Assortative Mixing in Networks
• Growing scale-free networks with small-world behavior
• Statistical mechanics of complex networks
• Evolution of networks
• The large-scale organization of metabolic networks
• On power-law relationships of the Internet topology

Cited by

• Scale-free networks generated by random walkers
• EVOLVING SCALE-FREE NETWORK MODEL WITH TUNABLE CLUSTERING
• Tuning degree distributions: Departing from scale-free networks
• Rate equation approach for correlations in growing network models
• Link-space formalism for network analysis
• Consensus formation on a triad scale-free network