Directed flag complex lifting (graph to simplicial complex) #44
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This pull request implements the directed clique (flag) complex lifting of a graph to a simplicial complex. The directed clique complex differs from its undirected counterpart in that it only accounts for k-simplices for which the (k+1)-clique is acyclic.
This implementation largely mirrors that of the clique complex lifting with the major change being an acceptance of directed networks as input data and the bookkeeping required to detect allowable simplices from each clique.
See the following references for more information on the directed clique complex.
[1] Reimann, Michael W., et al. "Cliques of neurons bound into cavities provide a missing link between structure and function." Frontiers in computational neuroscience 11 (2017): 266051.
[2] Lütgehetmann, Daniel, et al. "Computing persistent homology of directed flag complexes." Algorithms 13.1 (2020): 19.