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arXiv · 1309.7275

Superelliptical laws for complex networks

Stefano Allesina·Elizabeth Sander·Matthew J. Smith·Si Tang
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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.

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Stefano Allesina, Elizabeth Sander, Matthew J. Smith, Si Tang. 2013-11-07. Superelliptical laws for complex networks. https://arxiv.org/abs/1309.7275

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