A dissipative network model with neighboring activation |
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| Authors: | Fei Xiong Yun Liu Jiang Zhu Zhen Jiang Zhang Yan Chao Zhang Ying Zhang |
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| Institution: | (1) Department of Theoretical Physics, Institute of Physics, Budapest University of Technology, 8 Budafoki út, H-1111 Hungary,;(2) Laboratory of Physics, Helsinki University of Technology, P. O. Box 1100, FIN-02015 HUT, Finland; |
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| Abstract: | 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. |
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| Keywords: | |
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