Evolving Apollonian networks with small-world scale-free topologies

2005/11/30 by Zhongzhi Zhang, Lili Rong, Shuigeng Zhou · 3 citations
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #cond-mat.other #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.74.046105

published as Physical Review E 74, 046105 (2006) · 10 pages, 7 figures. Physical Review E, in press; available at http://link.aps.org/abstract/PRE/v74/e046105

arxiv created 2006/08/02 · openalex publication_date 2006/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose two types of evolving networks: evolutionary Apollonian networks (EANs) and general deterministic Apollonian networks (GDANs), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.

Citations

• Characterizing the network topology of the energy landscapes of atomic clusters
• Self-similar disk packings as model spatial scale-free networks
• Emergence of scaling in random networks
• The structure and function of complex networks

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