Superelliptical laws for complex networks
Populations and Evolution
2013-11-08 v2
Abstract
All dynamical systems of biological interest--be they food webs, regulation of genes, or contacts between healthy and infectious individuals--have complex network structure. Wigner's semicircular law and Girko's circular law describe the eigenvalues of systems whose structure is a fully connected network. However, these laws fail for systems with complex network structure. Here we show that in these cases the eigenvalues are described by superellipses. We also develop a new method to analytically estimate the dominant eigenvalue of complex networks.
Cite
@article{arxiv.1309.7275,
title = {Superelliptical laws for complex networks},
author = {Stefano Allesina and Elizabeth Sander and Matthew J. Smith and Si Tang},
journal= {arXiv preprint arXiv:1309.7275},
year = {2013}
}
Comments
28 pages, 16 figures, 2 tables