Spectral plot properties: Towards a qualitative classification of networks

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

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

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.
- Network classification,
- graph Laplacian,
- graph spectrum spectral plots,
- graph evolution
Citation: Anirban Banerjee, Jürgen Jost. Spectral plot properties: Towards a qualitative classification of networks[J]. Networks and Heterogeneous Media, 2008, 3(2): 395-411. doi: 10.3934/nhm.2008.3.395

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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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© 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)