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Spatially embedded random networks

journal contribution
posted on 2023-06-08, 11:39 authored by Lionel BarnettLionel Barnett, Ezequiel Di Paolo, S Bullock
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review E

ISSN

1539-3755

Publisher

American Physical Society

Issue

5

Volume

76

Page range

056115

Department affiliated with

  • Informatics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-05-21

First Compliant Deposit (FCD) Date

2012-05-18

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