---
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_identifier:
  - UT:000305348400006
  dct_language: eng
  dct_publisher: Public Library of Science@
  dct_title: Hierarchical ordering of reticular networks@
...