Physics – Physics and Society
Scientific paper
2009-12-22
Physica A 389 (2010) 1955-1964.
Physics
Physics and Society
Accepted for publication in Physica A
Scientific paper
10.1016/j.physa.2009.12.056
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases - usually associated with topological restrictions- their clustering is low and they are almost planar. In this paper we introduce a family of graphs which share all these properties and are defined by two parameters. As their construction is deterministic, we obtain exact analytic expressions for relevant properties of the graphs including the degree distribution, degree correlation, diameter, and average distance, as a function of the two defining parameters. Thus, the graphs are useful to model some complex networks, in particular several families of technological and biological networks, and in the design of new practical communication algorithms in relation to their dynamical processes. They can also help understanding the underlying mechanisms that have produced their particular structure.
Chen Lichao
Comellas Francesc
Miralles Alicia
Zhang Zhongzhi
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