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  Quantifying Loopy Network Architectures

Katifori, E., & Magnasco, M. O. (2012). Quantifying Loopy Network Architectures. PLoS ONE, 7(6): e37994. doi:10.1371/journal.pone.0037994.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-10C5-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-10C6-D
Genre: Journal Article

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 Creators:
Katifori, Eleni1, Author              
Magnasco, Marcelo O., Author
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1Max Planck Research Group Physics of Biological Organization, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063293              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2012-06-06
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: eDoc: 632400
DOI: 10.1371/journal.pone.0037994
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Title: PLoS ONE
  Alternative Title : PLOS ONE
Source Genre: Journal
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Pages: - Volume / Issue: 7 (6) Sequence Number: e37994 Start / End Page: - Identifier: -