Spectral densities of scale-free networks
Abstract
The spectral densities of the weighted Laplacian, random walk, and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent β. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and β.
- Publication:
-
Chaos
- Pub Date:
- June 2007
- DOI:
- 10.1063/1.2735019
- arXiv:
- arXiv:cond-mat/0703055
- Bibcode:
- 2007Chaos..17b6115K
- Keywords:
-
- 05.40.Fb;
- 05.70.Ce;
- 89.75.Hc;
- 02.10.Yn;
- 02.10.Ox;
- Random walks and Levy flights;
- Thermodynamic functions and equations of state;
- Networks and genealogical trees;
- Matrix theory;
- Combinatorics;
- graph theory;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 14 pages, two figures