Networks in life: Scaling properties and eigenvalue spectra

Abstract

We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and hierarchical organization of these graphs, a deterministic construction is also used. We demonstrate the use of determining the eigenvalue spectra of sparse random graph models for the categorization of small measured networks.

12 pages, 5 figures, last figure color

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• Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics
• Scaling Invariance in Spectra of Complex Networks: A Diffusion Factorial Moment Approach
• Origin and implications of zero degeneracy in networks spectra
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• Normal mode analysis of spectra of random networks
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