Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can be used to gain information otherwise concealed by the low-dimensional nature of graphs. We do this by extending previous work in homological persistence, and proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.

Mattia Bergomi, M.F. (2020). Topological graph persistence. COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS, 11(1), 72-87 [10.2478/caim-2020-0005].

Topological graph persistence

Mattia Bergomi;Massimo Ferri
;
2020

Abstract

Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can be used to gain information otherwise concealed by the low-dimensional nature of graphs. We do this by extending previous work in homological persistence, and proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.
2020
Mattia Bergomi, M.F. (2020). Topological graph persistence. COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS, 11(1), 72-87 [10.2478/caim-2020-0005].
Mattia Bergomi, Massimo Ferri, Lorenzo Zuffi
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/785374
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? ND
social impact