General model for Apollonian networks

Details General model for Apollonian networks General model for Apollonian networks

2005-12-11

arxiv.org/abs/cond-mat/0512229v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures

Scientific paper

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.

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