Research Article
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Year 2024, Early Access, 1 - 25
https://doi.org/10.15672/hujms.1317203

Abstract

References

  • [1] A. Adcock, E. Carlsson, and G. Carlsson, The ring of algebraic functions on persistence bar codes, arXiv preprint arXiv:1304.0530, 2013

Persistent Homology based Wasserstein distance for graph networks

Year 2024, Early Access, 1 - 25
https://doi.org/10.15672/hujms.1317203

Abstract

The technique of measuring similarity between topological spaces using Wasserstein distance
between persistence diagrams is extended to graph networks in this paper. A relationship
between the Wasserstein distance of the Cartesian product of topological spaces and the
Wasserstein distance of individual spaces is found to ease the comparative study of the
Cartesian product of topological spaces. The Cartesian product and the strong product of
weighted graphs are defined, and the relationship between the Wasserstein distance between
graph products and the Wasserstein distance between individual graphs is determined. For
this, clique complex filtration and the Vietoris- Rips filtration are used.

References

  • [1] A. Adcock, E. Carlsson, and G. Carlsson, The ring of algebraic functions on persistence bar codes, arXiv preprint arXiv:1304.0530, 2013
There are 1 citations in total.

Details

Primary Language English
Subjects Topology
Journal Section Mathematics
Authors

Archana Babu 0000-0002-8158-8373

Sunil Jacob John 0000-0002-6333-2884

Early Pub Date April 14, 2024
Publication Date
Published in Issue Year 2024 Early Access

Cite

APA Babu, A., & John, S. J. (2024). Persistent Homology based Wasserstein distance for graph networks. Hacettepe Journal of Mathematics and Statistics1-25. https://doi.org/10.15672/hujms.1317203
AMA Babu A, John SJ. Persistent Homology based Wasserstein distance for graph networks. Hacettepe Journal of Mathematics and Statistics. Published online April 1, 2024:1-25. doi:10.15672/hujms.1317203
Chicago Babu, Archana, and Sunil Jacob John. “Persistent Homology Based Wasserstein Distance for Graph Networks”. Hacettepe Journal of Mathematics and Statistics, April (April 2024), 1-25. https://doi.org/10.15672/hujms.1317203.
EndNote Babu A, John SJ (April 1, 2024) Persistent Homology based Wasserstein distance for graph networks. Hacettepe Journal of Mathematics and Statistics 1–25.
IEEE A. Babu and S. J. John, “Persistent Homology based Wasserstein distance for graph networks”, Hacettepe Journal of Mathematics and Statistics, pp. 1–25, April 2024, doi: 10.15672/hujms.1317203.
ISNAD Babu, Archana - John, Sunil Jacob. “Persistent Homology Based Wasserstein Distance for Graph Networks”. Hacettepe Journal of Mathematics and Statistics. April 2024. 1-25. https://doi.org/10.15672/hujms.1317203.
JAMA Babu A, John SJ. Persistent Homology based Wasserstein distance for graph networks. Hacettepe Journal of Mathematics and Statistics. 2024;:1–25.
MLA Babu, Archana and Sunil Jacob John. “Persistent Homology Based Wasserstein Distance for Graph Networks”. Hacettepe Journal of Mathematics and Statistics, 2024, pp. 1-25, doi:10.15672/hujms.1317203.
Vancouver Babu A, John SJ. Persistent Homology based Wasserstein distance for graph networks. Hacettepe Journal of Mathematics and Statistics. 2024:1-25.