Self-similar scale-free networks and disassortativity
Yook, SH, Radicchi, F, Meyer-Ortmanns, HPhys. Rev. E 72, 045105 (2005)
Times cited: 34
Abstract
Self-similar networks with scale-free degree distribution have recently
attracted much attention, since these apparently incompatible
properties were reconciled in [C. Song, S. Havlin, and H. A. Makse,
Nature 433, 392 (2005)] by an appropriate box-counting method that
enters the measurement of the fractal dimension. We study two genetic
regulatory networks (Saccharomyces cerevisiae [N. M. Luscombe, M. M.
Babu, H. Yu, M. Snyder, S. Teichmann, and M. Gerstein, Nature 431, 308
(2004)] and Escherichia coli
[http://www.ccg.unam.mx/Computational_Genomics/regulondb/DataSets/Regulo
nNetDataSets.html and http://www.gbf.de/SystemsBiology]) and show
their
self-similar and scale-free features, in extension to the datasets
studied by [C. Song, S. Havlin, and H. A. Makse, Nature 433, 392
(2005)]. Moreover, by a number of numerical results we support the
conjecture that self-similar scale-free networks are not assortative.
From our simulations so far these networks seem to be disassortative
instead. We also find that the qualitative feature of disassortativity
is scale-invariant under renormalization, but it appears as an
intrinsic feature of the renormalization prescription, as even
assortative networks become disassortative after a sufficient number of
renormalization steps.