2003/07/31 by Luciano da Fontoura Costa, LUCIANO DA FONTOURA COSTA
Engineering · Physics and Astronomy · #Complex Network Analysis Techniques #Theoretical and Computational Physics #Urban Design and Spatial Analysis #cond-mat
paper · pdf · doi:10.1142/s0129183104005619
arxiv created 2003/07/31 · openalex publication_date 2004/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.