Graph spectra as a systematic tool in computational biology

TL;DR

This paper introduces the spectrum of the normalized graph Laplacian as a systematic method for analyzing biological networks, revealing structural features and evolutionary hypotheses through spectral properties.

Contribution

It proposes using graph spectra as a new analytical tool in computational biology, linking spectral features to network formation and evolution.

Findings

Spectral properties reflect network formation processes.

Different biological networks exhibit characteristic spectral signatures.

Spectral analysis can generate hypotheses about network evolution.

Abstract

We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or duplication leave characteristic traces in the spectrum. This can suggest hypotheses about the evolution of a graph representing biological data. To this data, we analyze several biological networks in terms of rough qualitative data of their spectra.