Beyond Topological Persistence: Starting from Networks

Mattia G. Bergomi, Massimo Ferri, Pietro Vertechi and Lorenzo Zuffi
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Mattia G. Bergomi: Veos Digital, 20124 Milan, Italy
Massimo Ferri: Advanced Research Center on Electronic Systems “E. De Castro”, Department of Mathematics, Università di Bologna, 40126 Bologna, Italy
Pietro Vertechi: Veos Digital, 20124 Milan, Italy
Lorenzo Zuffi: Advanced Research Center on Electronic Systems “E. De Castro”, Department of Mathematics, Università di Bologna, 40126 Bologna, Italy

Mathematics, 2021, vol. 9, issue 23, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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