An alternative approach to determining average distance in a class of scale-free modular networks

Details An alternative approach to determining average distance in a class of scale-free modular networks An alternative approach to determining average distance in a class of scale-free modular networks

2009-11-18

arxiv.org/abs/0911.3454v1

Journal of Statistical Mechanics: Theory and Experiment, 2010, P12017

Physics

Physics and Society

Submitted for publicaction

Scientific paper

10.1088/1742-5468/2010/12/P12017

Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive relations derived from the self-similar structure of the networks, we compute rigorously this important quantity, obtaining an explicit closed-form solution, which recovers the previous result and is corroborated by extensive numerical calculations. The obtained exact expression shows that the average distance scales logarithmically with the number of nodes in the networks, indicating an existence of small-world behavior. We present that this small-world phenomenon comes from the peculiar architecture of the network family.

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