an:07293737
Zbl 07293737
Bergomi, Mattia G.; Ferri, Massimo; Zuffi, Lorenzo
Topological graph persistence
EN
Commun. Appl. Ind. Math. 11, No. 1, 72-87 (2020).
00449110
2020
j
55N31 05C10
clique; independent set; neighborhood; enclaveless set; Ramsey
Summary: 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.