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Grounded persistent path homology: a stable, topological descriptor for weighted digraphs

Abstract:

Weighted digraphs are used to model a variety of natural systems and can exhibit interesting structure across a range of scales. In order to understand and compare these systems, we require stable, interpretable, multiscale descriptors. To this end, we propose grounded persistent path homology (GrPPH)—a new, functorial, topological descriptor that describes the structure of an edge-weighted digraph via a persistence barcode. We show there is a choice of circuit basis for the graph which yields geometrically interpretable representatives for the features in the barcode. Moreover, we show the barcode is stable, in bottleneck distance, to both numerical and structural perturbations.

Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s10208-024-09679-2

Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
New College
Role:
Author
ORCID:
0000-0002-4395-5654
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0002-8076-7660


More from this funder
Funder identifier:
https://ror.org/0439y7842
Grant:
EP/R018472/1


Publisher:
Springer
Journal:
Foundations of Computational Mathematics More from this journal
Volume:
25
Issue:
5
Pages:
1711-1776
Publication date:
2024-08-23
Acceptance date:
2024-07-31
DOI:
EISSN:
1615-3383
ISSN:
1615-3375


Language:
English
Keywords:
Pubs id:
2025009
Local pid:
pubs:2025009
Deposit date:
2025-05-26
ARK identifier:

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