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Open AccessArticle

Computing Persistent Homology of Directed Flag Complexes

Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK
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Algorithms 2020, 13(1), 19; https://doi.org/10.3390/a13010019
Received: 27 November 2019 / Revised: 2 January 2020 / Accepted: 3 January 2020 / Published: 7 January 2020
(This article belongs to the Special Issue Topological Data Analysis)
We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology computation part of Flagser is based on the program Ripser by U. Bauer, but is optimised specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelisation by arbitrarily many cores. Flagser also has the option of working with undirected graphs. For homology computations Flagser has an approximate option, which shortens compute time with remarkable accuracy. We demonstrate the power of Flagser by applying it to the construction of the directed flag complex of digital reconstructions of brain microcircuitry by the Blue Brain Project and several other examples. In some instances we perform computation of homology. For a more complete performance analysis, we also apply Flagser to some other data collections. In all cases the hardware used in the computation, the use of memory and the compute time are recorded. View Full-Text
Keywords: neural networks; topology; directed graphs; directed flag complexes; persistent homology; computational software neural networks; topology; directed graphs; directed flag complexes; persistent homology; computational software
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Lütgehetmann, D.; Govc, D.; Smith, J.P.; Levi, R. Computing Persistent Homology of Directed Flag Complexes. Algorithms 2020, 13, 19.

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