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Properties Of An Evolving Directed Network With Local Rules And Intrinsic Variables

Author

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  • ANDRZEJ GRABOWSKI

    (Central Institute for Labour Protection - National Research Institute, Czerniakowska 16, 00-701 Warsaw, Poland;
    Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland)

  • ROBERT A. KOSIŃSKI

    (Central Institute for Labour Protection - National Research Institute, Czerniakowska 16, 00-701 Warsaw, Poland;
    Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland)

Abstract

We present a simple model of an evolving directed network based on local rules. It leads to a complex network with the properties of real systems, like scale-free distribution of outgoing and incoming connectivity, and a hierarchical structure. Each node is characterised by an intrinsic variableS, and the number of outgoing linkskout. As a result of network evolution the number of nodes and links (as well as their location) changes in time. For critical values of control parameters there is a transition to a scale-free network. Results for connectivity distribution found analytically agree with numerical calculations. Our model also reproduces other nontrivial properties of real networks, e.g. a large clustering coefficient and weak correlations between the age of a node and its connectivity. We have discovered an unexpected phenomenon that noise can increase the value of the clustering coefficient, whose large value is characteristic for a regular network.

Suggested Citation

  • Andrzej Grabowski & Robert A. Kosiński, 2007. "Properties Of An Evolving Directed Network With Local Rules And Intrinsic Variables," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 43-52.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:01:n:s0129183107010243
    DOI: 10.1142/S0129183107010243
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