Computing Persistent Homology of Directed Flag Complexes

Daniel Luetgehetmann, Dejan Govc, Jason Smith, Ran Levi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
3 Downloads (Pure)


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.
Original languageEnglish
Article number19
Issue number1
Publication statusPublished - 7 Jan 2020

Bibliographical note

This work was funded in part by an EPSRC grant EP/P025072/—“Topological Analysis of Neural Systems”.


  • math.AT
  • q-bio.NC
  • 55-04
  • Persistent homology
  • Neural networks
  • Directed graphs
  • Computational software
  • Topology
  • Directed flag complexes


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