Complexes of Tournaments in Directed Networks

Abstract: Clique graphs whose edges are oriented are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial sets, that we refer to as “tournaplexes", whose simplices are tournaments. In particular, given a directed graph 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 filtration on tournaplexes, and exploiting persistent homology, we observe that filtered flag tournaplexes provide finer means of distinguishing graph dynamics than the directed flag complex. We then demonstrate the power of those ideas by applying them to graph data arising from the Blue Brain Project’s digital reconstruction of a rat’s neocortex.

algebraic topology

Audience: researchers in the topic

Online algebraic topology seminar

Series comments: The seminar is hosted on Zoom. To minimise security concerns, access information for the Zoom meeting will only be sent out through the mailing list approximately an hour before the seminar is due to begin, details of which are below.

To join the mailing list for OATS, please complete the form here.