2005/12/11 by Zhongzhi Zhang, Zhang, Zhongzhi, Lili Rong +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Graph theory and applications #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0512229
5 pages, 2 figures
arxiv created 2005/12/11 · openalex publication_date 2005/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a general deterministic model for Apollonian Networks in an iterative fashion. The networks have small-world effect and scale-free topology. We calculate the exact results for the degree exponent, the clustering coefficient and the diameter. The major points of our results indicate that (a) the degree exponent can be adjusted in a wide range, (b) 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 (c) the diameter grows logarithmically with the number of network vertices.