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Quantifying Loopy Network Architectures
Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many differe...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2012
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3368948/ https://www.ncbi.nlm.nih.gov/pubmed/22701593 http://dx.doi.org/10.1371/journal.pone.0037994 |
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author | Katifori, Eleni Magnasco, Marcelo O. |
author_facet | Katifori, Eleni Magnasco, Marcelo O. |
author_sort | Katifori, Eleni |
collection | PubMed |
description | Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of approaches have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs. |
format | Online Article Text |
id | pubmed-3368948 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2012 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-33689482012-06-13 Quantifying Loopy Network Architectures Katifori, Eleni Magnasco, Marcelo O. PLoS One Research Article Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of approaches have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs. Public Library of Science 2012-06-06 /pmc/articles/PMC3368948/ /pubmed/22701593 http://dx.doi.org/10.1371/journal.pone.0037994 Text en Katifori, Magnasco. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Katifori, Eleni Magnasco, Marcelo O. Quantifying Loopy Network Architectures |
title | Quantifying Loopy Network Architectures |
title_full | Quantifying Loopy Network Architectures |
title_fullStr | Quantifying Loopy Network Architectures |
title_full_unstemmed | Quantifying Loopy Network Architectures |
title_short | Quantifying Loopy Network Architectures |
title_sort | quantifying loopy network architectures |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3368948/ https://www.ncbi.nlm.nih.gov/pubmed/22701593 http://dx.doi.org/10.1371/journal.pone.0037994 |
work_keys_str_mv | AT katiforieleni quantifyingloopynetworkarchitectures AT magnascomarceloo quantifyingloopynetworkarchitectures |