Spectral plots and the representation and interpretation of biological data

TL;DR

This paper introduces a spectral analysis method using normalized graph Laplacian spectra to visualize and compare biological networks, revealing distinctive properties and organization principles across different biological scales.

Contribution

It presents a novel spectral plot technique for analyzing biological networks, enabling systematic identification and visualization of shared and distinguishing features.

Findings

Spectral plots effectively differentiate biological network types.

Biological networks show distinctive spectral properties compared to theoretical models.

Universal properties are complemented by specific biological organization features.

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.