Graph spectra as a systematic tool in computational biology

Authors:
Anirban Banerjee;Jürgen Jost
Affiliations:
Max Planck Institute for Mathematics in the Sciences, Inselstreet 22, 04103 Leipzig, Germany;Max Planck Institute for Mathematics in the Sciences, Inselstreet 22, 04103 Leipzig, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

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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.