Self-similar planar graphs as models for complex networks

Details Self-similar planar graphs as models for complex networks Self-similar planar graphs as models for complex networks

2008-06-07

arxiv.org/abs/0806.1258v1

Physics

Physics and Society

10 pages, submitted to 19th International Workshop on Combinatorial Algorithms (IWOCA 2008)

Scientific paper

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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