Scaling invariance in spectra of complex networks: A diffusion factorial moment approach
Abstract
A new method called diffusion factorial moment is used to obtain scaling features embedded in the spectra of complex networks. For an Erdos-Renyi network with connecting probability pER<1/N , the scaling parameter is δ=0.51 , while for pER⩾1/N the scaling parameter deviates from it significantly. For WS small-world networks, in the special region prɛ[0.05,0.2] , typical scale invariance is found. For growing random networks, in the range of θɛ[0.33,049] , we have δ=0.6±0.1 . And the value of δ oscillates around δ=0.6 abruptly. In the range of θɛ[0.54,1] , we have basically δ>0.7 . Scale invariance is one of the common features of the three kinds of networks, which can be employed as a global measurement of complex networks in a unified way.
- Publication:
-
Physical Review E
- Pub Date:
- October 2005
- DOI:
- 10.1103/PhysRevE.72.046119
- arXiv:
- arXiv:cond-mat/0509012
- Bibcode:
- 2005PhRvE..72d6119Z
- Keywords:
-
- 89.75.-k;
- 05.45.-a;
- 02.60.-x;
- Complex systems;
- Nonlinear dynamics and chaos;
- Numerical approximation and analysis;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 6 pages, 8 figures. to appear in Physical Review E