Homological scaffold via minimal homology bases
Abstract The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one pr...
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| Auteurs principaux: | , , , , |
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| Format: | article |
| Langue: | EN |
| Publié: |
Nature Portfolio
2021
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| Accès en ligne: | https://doaj.org/article/22a7896fd70b47a09497c2280f34410c |
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| Résumé: | Abstract The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks. |
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