What statistical metrics to characterize karst network geometry and topology?

Pauline Collon and David Bernasconi and Cecile Vuilleumier and Philippe Renard. ( 2016 )
in: 2016 RING Meeting

Abstract

We propose to calculate various statistical metrics on a set of 31 3D actual karstic networks and 3 2D ones to assess their relevance for characterizing such natural systems. Some of these metrics aims at describing the network geometries while others relate to the network topology. The bias that can be induced by the field data acquisition technique is discussed. Part of the tested metrics were formerly proposed to characterize karstic systems but never tested on several actual networks. Other metrics are new proposals derived from graph theory or hydrology. To perform such an analysis, karst data were first converted to graphs consisting of nodes and links. A reduced version of this graph is also proposed to facilitate the topological analysis. The results allow to get a more intuitive understanding of various metrics, e.g. orientations, length entropy, degree of connectivity, cyclic coefficient, entropy of degrees, correlation of vertex degree - assortativity, average shortest path length, central point dominance... As a perspective, results provide an interesting dataset to compare with artificial networks.

Download / Links

BibTeX Reference

@INPROCEEDINGS{,
    author = { Collon, Pauline and Bernasconi, David and Vuilleumier, Cecile and Renard, Philippe },
     title = { What statistical metrics to characterize karst network geometry and topology? },
 booktitle = { 2016 RING Meeting },
      year = { 2016 },
  abstract = { We propose to calculate various statistical metrics on a set of 31 3D actual karstic networks and
3 2D ones to assess their relevance for characterizing such natural systems. Some of these metrics
aims at describing the network geometries while others relate to the network topology. The bias
that can be induced by the field data acquisition technique is discussed. Part of the tested metrics
were formerly proposed to characterize karstic systems but never tested on several actual networks.
Other metrics are new proposals derived from graph theory or hydrology. To perform such an
analysis, karst data were first converted to graphs consisting of nodes and links. A reduced version
of this graph is also proposed to facilitate the topological analysis. The results allow to get a more
intuitive understanding of various metrics, e.g. orientations, length entropy, degree of connectivity,
cyclic coefficient, entropy of degrees, correlation of vertex degree - assortativity, average shortest
path length, central point dominance... As a perspective, results provide an interesting dataset to
compare with artificial networks. }
}