Quantifying loopy network architectures.
Bottom Line:
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.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.
View Article:
PubMed Central - PubMed
Affiliation: Center for Studies in Physics and Biology, The Rockefeller University, New York, New York, United States of America. ekatifori@rockefeller.edu
ABSTRACT
Show MeSH
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. |
Related In:
Results -
Collection
getmorefigures.php?uid=PMC3368948&req=5
Mentions: The hierarchical decomposition framework if graphically represented in Fig. 2. The algorithm begins with a pruning step, where all tree-like components rooted on the loopy graph backbone, if present, are removed from the graph. This step eliminates all vertices that belong only to one edge, and produces a graph where each edge either separates or connects two loops (Fig. 3(a)). |
View Article: PubMed Central - PubMed
Affiliation: Center for Studies in Physics and Biology, The Rockefeller University, New York, New York, United States of America. ekatifori@rockefeller.edu