Self-similar planar graphs as models for complex networks

Lichao Chen; Francesc Comellas; Zhongzhi Zhang

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arXiv · 0806.1258

Self-similar planar graphs as models for complex networks

Lichao Chen·Francesc Comellas·Zhongzhi Zhang

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Abstract

In this paper we introduce a family of planar, modular and self-similar graphs which have small-world and scale-free properties. The main parameters of this family are comparable to those of networks associated to complex systems, and therefore the graphs are of interest as mathematical models for these systems. As the clustering coefficient of the graphs is zero, this family is an explicit construction that does not match the usual characterization of hierarchical modular networks, namely that vertices have clustering values inversely proportional to their degrees.

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Lichao Chen, Francesc Comellas, Zhongzhi Zhang. 2008-06-07. Self-similar planar graphs as models for complex networks. https://arxiv.org/abs/0806.1258

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