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Bioinformatics and Biomedical Engineering

Volume 9044 of the series Lecture Notes in Computer Science pp 395-405

Numerical Investigation of Graph Spectra and Information Interpretability of Eigenvalues

  • Hector ZenilAffiliated withUnit of Computational Medicine, Department of Medicine, Centre for Molecular Medicine, Karolinska Institute
  • , Narsis A. KianiAffiliated withUnit of Computational Medicine, Department of Medicine, Centre for Molecular Medicine, Karolinska Institute
  • , Jesper TegnérAffiliated withUnit of Computational Medicine, Department of Medicine, Centre for Molecular Medicine, Karolinska Institute

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Abstract

We undertake an extensive numerical investigation of the graph spectra of thousands regular graphs, a set of random Erdös-Rényi graphs, the two most popular types of complex networks and an evolving genetic network by using novel conceptual and experimental tools. Our objective in so doing is to contribute to an understanding of the meaning of the Eigenvalues of a graph relative to its topological and information-theoretic properties. We introduce a technique for identifying the most informative Eigenvalues of evolving networks by comparing graph spectra behavior to their algorithmic complexity. We suggest that extending techniques can be used to further investigate the behavior of evolving biological networks. In the extended version of this paper we apply these techniques to seven tissue specific regulatory networks as static example and network of a naïve pluripotent immune cell in the process of differentiating towards a Th17 cell as evolving example, finding the most and least informative Eigenvalues at every stage.

Keywords

Network science graph spectra behavior algorithmic probability information content algorithmic complexity Eigenvalues meaning