Exact Rank Reduction of Network Models

With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the bilinear structure of the matrix representation of the gene...

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Autores principales:	Eugenio Valdano, Alex Arenas
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2019
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/8397ad9ca0234499a408c98b1faab7f4
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spelling	oai:doaj.org-article:8397ad9ca0234499a408c98b1faab7f42021-12-02T11:40:45ZExact Rank Reduction of Network Models10.1103/PhysRevX.9.0310502160-3308https://doaj.org/article/8397ad9ca0234499a408c98b1faab7f42019-09-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.9.031050http://doi.org/10.1103/PhysRevX.9.031050https://doaj.org/toc/2160-3308With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the bilinear structure of the matrix representation of the generative model, we separate its null eigenspace and reduce the exact description of the generative model to a smaller vector space. After reduction, we group generative models in universality classes according to their rank and metric signature and work out, in a computationally affordable way, their relevant properties (e.g., spectrum). The reduction also provides the environment for a simplified computation of their properties. The proposed scheme works for any generative model admitting a matrix representation and will be very useful in the study of dynamical processes on networks, as well as in the understanding of generative models to come, according to the provided classification.Eugenio ValdanoAlex ArenasAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 9, Iss 3, p 031050 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Eugenio Valdano Alex Arenas Exact Rank Reduction of Network Models
description	With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the bilinear structure of the matrix representation of the generative model, we separate its null eigenspace and reduce the exact description of the generative model to a smaller vector space. After reduction, we group generative models in universality classes according to their rank and metric signature and work out, in a computationally affordable way, their relevant properties (e.g., spectrum). The reduction also provides the environment for a simplified computation of their properties. The proposed scheme works for any generative model admitting a matrix representation and will be very useful in the study of dynamical processes on networks, as well as in the understanding of generative models to come, according to the provided classification.
format	article
author	Eugenio Valdano Alex Arenas
author_facet	Eugenio Valdano Alex Arenas
author_sort	Eugenio Valdano
title	Exact Rank Reduction of Network Models
title_short	Exact Rank Reduction of Network Models
title_full	Exact Rank Reduction of Network Models
title_fullStr	Exact Rank Reduction of Network Models
title_full_unstemmed	Exact Rank Reduction of Network Models
title_sort	exact rank reduction of network models
publisher	American Physical Society
publishDate	2019
url	https://doaj.org/article/8397ad9ca0234499a408c98b1faab7f4
work_keys_str_mv	AT eugeniovaldano exactrankreductionofnetworkmodels AT alexarenas exactrankreductionofnetworkmodels
_version_	1718395527106658304

Exact Rank Reduction of Network Models

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