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Diophantine Networks

Bedogné, C; Masucci, AP; Rodgers, GJ; (2007) Diophantine Networks. Physica A , 387 2161 - ?. 10.1016/j.physa.2007.11.038.

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Abstract

We introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by representing integers as vertices and by drawing cliques between M vertices every time that M distinct integers satisfy the equation. We analyse the network generated by the Pythagorean equation $x^{2}+y^{2}= z^{2}$ showing that its degree distribution is well approximated by a power law with exponential cut-off. We also show that the properties of this network differ considerably from the features of scale-free networks generated through preferential attachment. Remarkably we also recover a power law for the clustering coefficient.

Type:Article
Title:Diophantine Networks
DOI:10.1016/j.physa.2007.11.038
Publisher version:http://dx.doi.org/10.1016/j.physa.2007.11.038
UCL classification:UCL > School of BEAMS > Faculty of the Built Environment > Centre for Advanced Spatial Analysis

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