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Planar growth generates scale-free networks

Planar growth generates scale-free networks
Planar growth generates scale-free networks
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in R 2 , forming new connections to old nodes subject to the constraint that edges do not cross. The resulting network has a power law degree distribution, high clustering and the small world property. We argue that these characteristics are a consequence of the two defining features of the network formation procedure; growth and planarity conservation. We demonstrate that the model can be understood as a variant of random Apollonian growth and further propose a one parameter family of models with the Random Apollonian Network and the Deterministic Apollonian Network as extreme cases and our model as a midpoint between them. We then relax the planarity constraint by allowing edge crossings with some probability and find a smooth crossover from power law to exponential degree distributions when this probability is increased.
2051-1310
1-26
Haslett, Garvin
200072f7-9cae-43ab-82d4-bbc983ff8629
Bullock, Seth
eeb8c2f8-dd55-4ddf-aa8d-24d77b6fe1b3
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Haslett, Garvin
200072f7-9cae-43ab-82d4-bbc983ff8629
Bullock, Seth
eeb8c2f8-dd55-4ddf-aa8d-24d77b6fe1b3
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7

Haslett, Garvin, Bullock, Seth and Brede, Markus (2016) Planar growth generates scale-free networks. Journal of Complex Networks, 1-26. (doi:10.1093/comnet/cnw005). (In Press)

Record type: Article

Abstract

In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in R 2 , forming new connections to old nodes subject to the constraint that edges do not cross. The resulting network has a power law degree distribution, high clustering and the small world property. We argue that these characteristics are a consequence of the two defining features of the network formation procedure; growth and planarity conservation. We demonstrate that the model can be understood as a variant of random Apollonian growth and further propose a one parameter family of models with the Random Apollonian Network and the Deterministic Apollonian Network as extreme cases and our model as a midpoint between them. We then relax the planarity constraint by allowing edge crossings with some probability and find a smooth crossover from power law to exponential degree distributions when this probability is increased.

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Accepted/In Press date: 20 January 2016
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 388773
URI: http://eprints.soton.ac.uk/id/eprint/388773
ISSN: 2051-1310
PURE UUID: 04bd41b9-bfa6-4958-a060-3f7e1496c475

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Date deposited: 03 Mar 2016 11:11
Last modified: 20 Jul 2019 06:04

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