American Institute of Mathematical Sciences

Advanced
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

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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