<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Topological graph persistence

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Topological graph persistence"}

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...

Topological graph persistence

Publié en ligne: 06 déc. 2020

Pages: 72 - 87

Reçu: 28 avr. 2020

Accepté: 11 sept. 2020

DOI: https://doi.org/10.2478/caim-2020-0005

Mots clés
Clique, independent set, neighborhood, enclaveless set, Ramsey

© 2020 Mattia G. Bergomi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Topological graph persistence

Publié en ligne: 06 déc. 2020

Pages: 72 - 87

Reçu: 28 avr. 2020

Accepté: 11 sept. 2020

DOI: https://doi.org/10.2478/caim-2020-0005

Mots clésClique, independent set, neighborhood, enclaveless set, Ramsey

© 2020 Mattia G. Bergomi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Clique, independent set, neighborhood, enclaveless set, Ramsey