Diophantine Networks
Physics and Society
2009-11-13 v1 Disordered Systems and Neural Networks
Data Analysis, Statistics and Probability
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 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.
Keywords
Cite
@article{arxiv.0712.1723,
title = {Diophantine Networks},
author = {C. Bedogné and A. P. Masucci and G. J. Rodgers},
journal= {arXiv preprint arXiv:0712.1723},
year = {2009}
}