Spectral plot properties: Towards a qualitative classification of networks

Anirban Banerjee; Jürgen Jost

doi:10.3934/nhm.2008.3.395

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2008, Volume 3, Issue 2: 395-411. Doi: 10.3934/nhm.2008.3.395

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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

Received: August 2007

Revised: February 2008

Published online: March 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 05C75, 47A75; Secondary: 90C35, 68R10.

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