Preprint Article Version 1 This version is not peer-reviewed

Complexes of Tournaments, Directionality Filtrations and Persistent Homology

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. Preprints 2020, 2020030068 (doi: 10.20944/preprints202003.0068.v1). Levi, R.; Govc, D.; Smith, J. Complexes of Tournaments, Directionality Filtrations and Persistent Homology. Preprints 2020, 2020030068 (doi: 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.

Subject Areas

Tournaments; Semi-Simplicial Sets; Neural networks; Persistent homology

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.