Deterministic Scale-free Networks Created in a Recursive Manner

2005/12/07 by Zhongzhi Zhang, Lili Rong
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Graph theory and applications #Interconnection Networks and Systems #cond-mat.other #cond-mat.stat-mech

paper · pdf · doi:10.1109/icccas.2006.285223

published as Communications, Circuits and Systems Proceedings, 2006 International Conference on Volume 4, June 2006 Page(s): 2683-2686 · 5 pages, 2 figures

arxiv created 2005/12/07 · openalex publication_date 2006/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering coefficient and the diameter. The major points of our results indicate: the degree exponent can be adjusted; the clustering coefficient of each individual vertex is inversely proportional to its degree and the average clustering coefficient of all vertices approaches to a nonzero value in the infinite network order; and the diameter grows logarithmically with the number of network vertices.

Citations

• Evolving Apollonian networks with small-world scale-free topologies
• Self-similar disk packings as model spatial scale-free networks
• Emergence of Scaling in Random Networks
• Flexible construction of hierarchical scale-free networks with general exponent
• Statistical mechanics of complex networks
• Evolution of networks
• The structure and function of complex networks