Spatially embedded random networks

Barnett, L, Di Paolo, E and Bullock, S (2007) Spatially embedded random networks. Physical Review E, 76 (5). 056115. ISSN 1539-3755

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Many real-world networks analysed 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 specialised 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 analyse 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 (SERN) 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.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
Subjects: Q Science > QA Mathematics > QA0276 Mathematical statistics
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Lionel Barnett
Date Deposited: 21 May 2012 07:55
Last Modified: 02 Jul 2019 21:04

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