Spectral plots and the representation and interpretation of biological data

Abstract

It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or foodwebs, and that on the other hand distinguish them from other structures. We introduce and apply a general method, based on the spectrum of the normalized graph Laplacian, that yields repre- sentations, the spectral plots, that allow us to find and visualize such properties systematically. We present such visualizations for a wide range of biological networks and compare them with those for networks derived from theoretical schemes. The differences that we find are quite striking and suggest that the search for universal properties of biological networks should be complemented by an understanding of more specific features of biological organization principles at different scales.

15 pages, 7 figures

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• Discovering Global Patterns in Linguistic Networks through Spectral Analysis: A Case Study of the Consonant Inventories
• An introduction to spectral distances in networks (extended version)
• Constructing transient amplifiers for death-Birth updating: A case study of cubic and quartic regular graphs