[ONLINE] ATA Lab Seminar: "Complexes of Tournaments in Directed Networks"

Speaker - Professor Ran Levi,  The School of Natural and Computing Sciences, University of Aberdeen

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.