Version 1
: Received: 2 March 2020 / Approved: 4 March 2020 / Online: 4 March 2020 (11:40:12 CET)
How to cite:
Levi, R.; Govc, D.; Smith, J. Complexes of Tournaments, Directionality Filtrations and Persistent Homology. Preprints2020, 2020030068. https://doi.org/10.20944/preprints202003.0068.v1
Levi, R.; Govc, D.; Smith, J. Complexes of Tournaments, Directionality Filtrations and Persistent Homology. Preprints 2020, 2020030068. https://doi.org/10.20944/preprints202003.0068.v1
Levi, R.; Govc, D.; Smith, J. Complexes of Tournaments, Directionality Filtrations and Persistent Homology. Preprints2020, 2020030068. https://doi.org/10.20944/preprints202003.0068.v1
APA Style
Levi, R., Govc, D., & Smith, J. (2020). Complexes of Tournaments, Directionality Filtrations and Persistent Homology. Preprints. https://doi.org/10.20944/preprints202003.0068.v1
Chicago/Turabian Style
Levi, R., Dejan Govc and Jason Smith. 2020 "Complexes of Tournaments, Directionality Filtrations and Persistent Homology" Preprints. https://doi.org/10.20944/preprints202003.0068.v1
Abstract
Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as ``tournaplexes'', whose simplices are tournaments. In particular, given a digraph G, we associate with it a ``flag tournaplex'' which is a tournaplex containing the directed flag complex of G, but also the geometric realisation of cliques that are not directed. We define several types of filtrations on tournaplexes, and exploiting persistent homology, we observe that flag tournaplexes provide finer means of distinguishing graph dynamics than the directed flag complex. We then demonstrate the power of these ideas by applying them to graph data arising from the Blue Brain Project's digital reconstruction of a rat's neocortex.
Computer Science and Mathematics, Geometry and Topology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
