Physics – Physics and Society
Scientific paper
2007-12-11
Physica A vol.387, 2161 (2008).
Physics
Physics and Society
Scientific paper
10.1016/j.physa.2007.11.038
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.
Bedogné C.
Masucci Adolfo Paolo
Rodgers Geoff J.
No associations
LandOfFree
Diophantine Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Diophantine Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diophantine Networks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-474410