Computer Science – Computational Engineering – Finance – and Science
Scientific paper
2010-05-09
Eur. Phys. J. B 79, 115-120 (2011)
Computer Science
Computational Engineering, Finance, and Science
RevTex 6 pages, 7 figs, linked to arXiv:1003.5455[cs.SE]. Research at http://www.quantware.ups-tlse.fr/, Improved version, cha
Scientific paper
10.1140/epjb/e2010-10774-7
We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be $\nu \approx 0.63$ that corresponds to the fractal dimension of the network $d \approx 1.2$. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension $d<2$.
Chepelianskii Alexei D.
Ermann Leonardo
Shepelyansky Dima L.
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