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phlite_grpph

This library uses phlite to compute grounded persistent path homology (GrPPH) [1]. We expose Python bindings to two python functions: grpph and grpph_with_involution.

Both functions accept two arguments nodes and edges. The first, nodes, should be an integer: the number of nodes in your weighted digraph. The second, edges, should be a list of tuples (i, j, w) representing an edge from node i to node j with weight w.

The first function returns two values: essential and pairings. The second function additionally returns reps. The first two return values are the GrPPH barcode. The reps return value is a list of cycle representatives: one for each finite feature in degree 1.

For example usage, see reps.py and example.py or get in touch.

References

[1] Chaplin, T., Harrington, H.A. and Tillmann, U., 2022. Grounded persistent path homology: a stable, topological descriptor for weighted digraphs. arXiv preprint arXiv:2210.11274.

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