Spatially embedded random networks

Lionel Barnett, Ezequiel Di Paolo, Seth Bullock

Research output: Contribution to journalArticle (Academic Journal)peer-review

39 Citations (Scopus)

Abstract

Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples.
Original languageEnglish
Article number056115
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume76
Issue number5
DOIs
Publication statusPublished - 20 Nov 2007

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