arXiv:2502.02151 Abstract | arXiv Analytics

arXiv:2502.02151 [math.AT]Abstract References Reviews Resources

Persistent Homology on a lattice of multigraphs

Published 2025-02-04Version 1

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.

Comments: arXiv admin note: text overlap with arXiv:2308.16630

Categories: math.AT, q-bio.NC

Keywords: persistent homology, original example, multicomplex structure, betti numbers, incremental algorithm

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