High-dimensional random Apollonian networks

2005/02/28 by Zhongzhi Zhang, Lili Rong, Francesc Comellas · 1 citation
Computer Science · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #Topological and Geometric Data Analysis #cond-mat.other

paper · pdf · doi:10.1016/j.physa.2005.09.042

arxiv created 2005/05/22 · openalex publication_date 2005/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation results and comparable to those coming from real networks. We prove also analitically that the average path length of the networks increases at most logarithmically with the number of vertices.

Citations

• Random Apollonian Networks
• Self-similar disk packings as model spatial scale-free networks
• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Evolution of networks
• Maximal planar networks with large clustering coefficient and power-law degree distribution
• The large-scale organization of metabolic networks
• The structure and function of complex networks
• On power-law relationships of the Internet topology

Cited by

• Dynamics and processing in finite self-similar networks