Fractal Weyl law for Linux Kernel architecture
Laboratoire de Physique Théorique (IRSAMC),
Université de Toulouse, UPS-CNRS, 31062 Toulouse, France
2 LPS, Université Paris-Sud, CNRS, UMR8502, 91405 Orsay, France
Corresponding author: a firstname.lastname@example.org
Published online: 21 December 2010
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 ν ≈ 0.65 that corresponds to the fractal dimension of the network d ≈ 1.3. An independent computation of the fractal dimension by the cluster growing method, generalized for directed networks, gives a close value d ≈ 1.4. 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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010