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Spatially embedded random networks

Barnett, Lionel, Di Paolo, Ezequiel and Bullock, Seth (2007) Spatially embedded random networks Physical Review E, 76, (5)

Record type: Article


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.

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Published date: 2007
Organisations: Agents, Interactions & Complexity


Local EPrints ID: 266764
ISSN: 1539-3755
PURE UUID: 809f004e-d5b1-49c8-918e-129d4c3b26b7

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Date deposited: 07 Oct 2008 14:57
Last modified: 18 Jul 2017 07:12

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Author: Lionel Barnett
Author: Ezequiel Di Paolo
Author: Seth Bullock

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