The effect of disorder on the hierarchical modularity in complex systems

Details The effect of disorder on the hierarchical modularity in complex systems The effect of disorder on the hierarchical modularity in complex systems

2005-06-16

arxiv.org/abs/cond-mat/0506395v2

Physics

Condensed Matter

Statistical Mechanics

16 pages, 13 figures, to be published in Fractals. Description of the algorithm has been changed

Scientific paper

We consider a system hierarchically modular, if besides its hierarchical structure it shows a sequence of scale separations from the point of view of some functionality or property. Starting from regular, deterministic objects like the Vicsek snowflake or the deterministic scale free network by Ravasz et al. we first characterize the hierarchical modularity by the periodicity of some properties on a logarithmic scale indicating separation of scales. Then we introduce randomness by keeping the scale freeness and other important characteristics of the objects and monitor the changes in the modularity. In the presented examples sufficient amount of randomness destroys hierarchical modularity. Our findings suggest that the experimentally observed hierarchical modularity in systems with algebraically decaying clustering coefficients indicates a limited level of randomness.

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