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.Comment: 10 pages, submitted to 19th International Workshop on Combinatorial
Algorithms (IWOCA 2008
