Topology and correlations in structured scale-free networks

2002/09/07 by Alexei Vazquez, Alexei Vázquez, Marián Boguñá +5 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Graph theory and applications #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.67.046111

published as Phys. Rev. E 67, 046111 (2003) · 10 pages, 9 figures

arxiv created 2002/09/07 · openalex publication_date 2003/04/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a recently introduced class of scale-free networks showing a high clustering coefficient and nontrivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small-world properties in the whole parameter range. We discuss the physical properties of these networks in the light of the present detailed analysis.

Citations

• Emergence of Scaling in Random Networks
• Epidemic Threshold in Structured Scale-Free Networks
• Growing scale-free networks with small-world behavior
• Error and attack tolerance of complex networks
• Statistical mechanics of complex networks
• Evolution of networks
• On power-law relationships of the Internet topology

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