%0 Journal Article
%T Motif based hierarchical random graphs: structural properties and critical points of an Ising model
%A M. Kotorowicz
%J Condensed Matter Physics
%D 2011
%I Institute for Condensed Matter Physics
%X A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, vol. 298, 824 ¨C 827]. The construction scheme resembles that used in [Hinczewski M., A. Nihat Berker, Phys. Rev. E, 2006, vol. 73, 066126], according to which the short-range bonds are non-random, whereas the long-range bonds appear independently with the same probability. A number of structural properties of the graphs have been described, among which there are degree distributions, clustering, amenability, small-world property. For one of the motifs, the critical point of the Ising model defined on the corresponding graph has been studied.
%K amenability
%K degree distribution
%K clustering
%K small-world graph
%K Ising model
%K critical point
%U http://dx.doi.org/10.5488/CMP.14.13801