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.
@article{arxiv.1707.09670,
title = {Topological Graph Persistence},
author = {Mattia G. Bergomi and Massimo Ferri and Lorenzo Zuffi},
journal= {arXiv preprint arXiv:1707.09670},
year = {2018}
}