Persistent Homology on a lattice of multigraphs

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1. Verfasser: Boils, Joaquin Diaz
Format: Preprint
Veröffentlicht: 2025
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author Boils, Joaquin Diaz
author_facet Boils, Joaquin Diaz
contents A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of Persistent Homology in this context, its interaction with the ordering and the repercussions of the process of merging multigraphs in the calculation of the Betti numbers. For the latter, an extended version of the incremental algorithm is provided. The ideas here developed are mainly oriented to the original example described in [10] and used more extensively in [11] in the context of the formalization of the notion of embodiment in Neuroscience.
format Preprint
id arxiv_https___arxiv_org_abs_2502_02151
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Persistent Homology on a lattice of multigraphs
Boils, Joaquin Diaz
Algebraic Topology
Neurons and Cognition
A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of Persistent Homology in this context, its interaction with the ordering and the repercussions of the process of merging multigraphs in the calculation of the Betti numbers. For the latter, an extended version of the incremental algorithm is provided. The ideas here developed are mainly oriented to the original example described in [10] and used more extensively in [11] in the context of the formalization of the notion of embodiment in Neuroscience.
title Persistent Homology on a lattice of multigraphs
topic Algebraic Topology
Neurons and Cognition
url https://arxiv.org/abs/2502.02151