Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/1323
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dc.contributor.authorBedogne, C-
dc.contributor.authorMasucci, AP-
dc.contributor.authorRodgers, GJ-
dc.coverage.spatial9en
dc.date.accessioned2007-11-19T14:48:28Z-
dc.date.available2007-11-19T14:48:28Z-
dc.date.issued2007-
dc.identifier.citationPhysica A: Statistical Mechanics and its Applicationsen
dc.identifier.uriwww.elsevier.com/locate/physaen
dc.identifier.urihttp://bura.brunel.ac.uk/handle/2438/1323-
dc.description.abstractWe 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 rep- resenting integers as vertices and by drawing cliques between M vertices every time that M dis- tinct integers satisfy the equation. We analyse the network generated by the Pythagorean equation x2+y2 = z2 showing that its degree distribution is well approximated by a power law with exponen- tial cut-o®. We also show that the properties of this network di®er considerably from the features of scale-free networks generated through preferential attachment. Remarkably we also recover a power law for the clustering coe±cient. We then study the network associated with the equation x2 + y2 = z showing that the degree distribution is consistent with a power-law for several decades of values of k and that, after having reached a minimum, the distribution begins rising again. The power law exponent, in this case, is given by ° » 4:5 We then analyse clustering and ageing and compare our results to the ones obtained in the Pythagorean case.en
dc.format.extent1648986 bytes-
dc.format.mimetypeapplication/pdf-
dc.language.isoen-
dc.publisherElsevieren
dc.titleDiophantine networksen
dc.typePreprinten
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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