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Mathematics
Volume 9
Issue 23
10.3390/math9233079
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Article

Beyond Topological Persistence: Starting from Networks

by
Mattia G. Bergomi
1,
Massimo Ferri
2,*,
Pietro Vertechi
1 and
Lorenzo Zuffi
2
1
Veos Digital, 20124 Milan, Italy
2
Advanced Research Center on Electronic Systems “E. De Castro”, Department of Mathematics, Università di Bologna, 40126 Bologna, Italy
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(23), 3079; https://doi.org/10.3390/math9233079
Submission received: 9 October 2021 / Revised: 22 November 2021 / Accepted: 28 November 2021 / Published: 29 November 2021
(This article belongs to the Section E: Applied Mathematics)
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Abstract

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and digraphs. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness—clique communities, k-vertex, and k-edge connectedness—directly on simple graphs and strong connectedness in digraphs.
Keywords: categorical persistence function; connectedness; persistence diagram; poset; graph; digraph categorical persistence function; connectedness; persistence diagram; poset; graph; digraph

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MDPI and ACS Style

Bergomi, M.G.; Ferri, M.; Vertechi, P.; Zuffi, L. Beyond Topological Persistence: Starting from Networks. Mathematics 2021, 9, 3079. https://doi.org/10.3390/math9233079

AMA Style

Bergomi MG, Ferri M, Vertechi P, Zuffi L. Beyond Topological Persistence: Starting from Networks. Mathematics. 2021; 9(23):3079. https://doi.org/10.3390/math9233079

Chicago/Turabian Style

Bergomi, Mattia G., Massimo Ferri, Pietro Vertechi, and Lorenzo Zuffi. 2021. "Beyond Topological Persistence: Starting from Networks" Mathematics 9, no. 23: 3079. https://doi.org/10.3390/math9233079

APA Style

Bergomi, M. G., Ferri, M., Vertechi, P., & Zuffi, L. (2021). Beyond Topological Persistence: Starting from Networks. Mathematics, 9(23), 3079. https://doi.org/10.3390/math9233079

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