2017/07/30 by Bergomi, Mattia G., Ferri, Massimo, Zuffi, Lorenzo · 2 citations
#05C10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.09670
Graphs are a basic tool for the representation of modern data. 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 that by extending previous work of other researchers in homological persistence, by proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.