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Topology"],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as \u201ctournaplexes\u201d, whose simplices are tournaments. In particular, given a digraph <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {G}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>G<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, we associate with it a \u201cflag tournaplex\u201d which is a tournaplex containing the directed flag complex of <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {G}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>G<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, 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\u2019s digital reconstruction of a rat\u2019s neocortex.<\/jats:p>","DOI":"10.1007\/s41468-021-00068-0","type":"journal-article","created":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T10:10:03Z","timestamp":1618827003000},"page":"313-337","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Complexes of tournaments, directionality filtrations and persistent homology"],"prefix":"10.1007","volume":"5","author":[{"given":"Dejan","family":"Govc","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5297-8295","authenticated-orcid":false,"given":"Ran","family":"Levi","sequence":"additional","affiliation":[]},{"given":"Jason P.","family":"Smith","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,19]]},"reference":[{"issue":"1\/2","key":"68_CR1","doi-asserted-by":"publisher","first-page":"265","DOI":"10.2307\/2333494","volume":"49","author":"G Alway","year":"1962","unstructured":"Alway, G.: The distribution of the number of circular triads in paired comparisons. 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