--- res: bibo_abstract: - The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the "root" of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Yuriy foaf_name: Mileyko, Yuriy foaf_surname: Mileyko - foaf_Person: foaf_givenName: Herbert foaf_name: Edelsbrunner, Herbert foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Charles foaf_name: Price, Charles foaf_surname: Price - foaf_Person: foaf_givenName: Joshua foaf_name: Weitz, Joshua foaf_surname: Weitz bibo_doi: 10.1371/journal.pone.0036715 bibo_issue: '6' bibo_volume: 7 dct_date: 2012^xs_gYear dct_language: eng dct_publisher: Public Library of Science@ dct_title: Hierarchical ordering of reticular networks@ ...