Spectral plot properties: Towards a qualitative classification of networks

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June 2008, 3(2): 395-411. doi: 10.3934/nhm.2008.3.395

Spectral plot properties: Towards a qualitative classification of networks

Anirban Banerjee ^1, and Jürgen Jost ^1,

1.	Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany

Received August 2007 Revised February 2008 Published March 2008

Abstract
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We introduce a tentative classification scheme for empirical networks based on global qualitative properties detected through the spectrum of the Laplacian of the graph underlying the network. Our method identifies several distinct types of networks across different domains of applications, indicates hidden regularity properties and provides evidence for processes like node duplication behind the evolution or construction of a given class of networks.

Keywords: graph Laplacian, Network classification, graph evolution, graph spectrum spectral plots.

Mathematics Subject Classification: Primary: 05C75, 47A75; Secondary: 90C35, 68R1.

Citation: Anirban Banerjee, Jürgen Jost. Spectral plot properties: Towards a qualitative classification of networks. Networks & Heterogeneous Media, 2008, 3 (2) : 395-411. doi: 10.3934/nhm.2008.3.395

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