Journal article
Grounded persistent path homology: a stable, topological descriptor for weighted digraphs
- Abstract:
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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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(Preview, Version of record, pdf, 1.4MB, Terms of use)
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- Publisher copy:
- 10.1007/s10208-024-09679-2
Authors
- 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:
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1615-3383
- ISSN:
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1615-3375
- Language:
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English
- Keywords:
- Pubs id:
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2025009
- Local pid:
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pubs:2025009
- Deposit date:
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2025-05-26
- ARK identifier:
Terms of use
- Copyright holder:
- Chaplin et al.
- Copyright date:
- 2024
- Rights statement:
- Copyright © 2024, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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