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THE EFFECT OF DISORDER ON THE HIERARCHICAL MODULARITY IN COMPLEX SYSTEMS

Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary

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G. TIBÉLY

Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary

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J. KERTÉSZ

Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary

Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9400, FIN-02015 HUT, Finland

Corresponding author.

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https://doi.org/10.1142/S0218348X06003143Cited by:0 (Source: Crossref)

Abstract

Hierarchically modular systems show a sequence of scale separations in some functionality or property in addition to their hierarchical topology. 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, a 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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