On scale-free and poly-scale behaviors of random hierarchical network

Details On scale-free and poly-scale behaviors of random hierarchical network On scale-free and poly-scale behaviors of random hierarchical network

2008-11-27

arxiv.org/abs/0811.4518v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 6 figures (paper is substantially revised)

Scientific paper

In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In particular, we compute numerically the spectral density of large random adjacency matrices defined by a hierarchy of the Bernoulli distributions $\{q_1,q_2,...\}$ on matrix elements, where $q_{\gamma}$ depends on hierarchy level $\gamma$ as $q_{\gamma}=p^{-\mu \gamma}$ ($\mu>0$). For the spectral density we clearly see the free--scale behavior. We show also that for the Gaussian distributions on matrix elements with zero mean and variances $\sigma_{\gamma}=p^{-\nu \gamma}$, the tail of the spectral density, $\rho_G(\lambda)$, behaves as $\rho_G(\lambda) \sim |\lambda|^{-(2-\nu)/(1-\nu)}$ for $|\lambda|\to\infty$ and $0<\nu<1$, while for $\nu\ge 1$ the power--law behavior is terminated. We also find that the vertex degree distribution of such hierarchical networks has a poly--scale fractal behavior extended to a very broad range of scales.

Affiliated with

Also associated with

No associations

Rating

On scale-free and poly-scale behaviors of random hierarchical network does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On scale-free and poly-scale behaviors of random hierarchical network, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On scale-free and poly-scale behaviors of random hierarchical network will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-232633