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Exploring Graph and Digraph Persistence
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These authors have contributed equally to this work.
Version 1
: Received: 30 August 2023 / Approved: 30 August 2023 / Online: 31 August 2023 (02:24:52 CEST)
A peer-reviewed article of this Preprint also exists.
Bergomi, M.G.; Ferri, M. Exploring Graph and Digraph Persistence. Algorithms 2023, 16, 465. Bergomi, M.G.; Ferri, M. Exploring Graph and Digraph Persistence. Algorithms 2023, 16, 465.
Abstract
Among the various generalizations of persistent topology, the one based on rank functions and leading to indexing-aware functions appears to be particularly suited to catch graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies "simple" and "single-vertex" features in directed and undirected graphs, by which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the "sink" feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.
Keywords
Persistence; categorical persistence functions; indexing-aware persistence functions; steady set; ranging set; weighted graph; weighted digraph
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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