VORONOI AND FRACTAL COMPLEX NETWORKS AND THEIR CHARACTERIZATION

Luciano Da Fontoura Costa ()
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Luciano Da Fontoura Costa: Institute of Physics of São Carlos, University of São Paulo, São Carlos, SP, Caixa Postal 369, 13560-970, Brasil

International Journal of Modern Physics C (IJMPC), 2004, vol. 15, issue 01, 175-183

Abstract: Real world networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a natural means for relating such networks with metric spaces, but also a natural means for obtaining fractal complex networks. A series of comprehensive measurements closely related to spatial aspects of these networks is proposed, which includes the effective length, adjacency, as well as the fractal dimension of the network in terms of the spatial scales defined by successive shortest paths starting from a specific node. The potential of such features is illustrated with respect to the random, small-world, scale-free and fractal network models.

Keywords: Complex networks; spatial restrictions; Voronoi tessellations; hierarchical structures; fractal dimension (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0129183104005619

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