Steady and ranging sets in graph persistence
Computational Geometry
2022-08-30 v3 Combinatorics
Abstract
Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and \textit{ranging} sets: two standardized ways of producing persistence diagrams directly from graph-theoretical features. The two constructions are framed in the context of \textit{indexing-aware persistence functions}. Furthermore, we introduce a sufficient condition for stability. Finally, we apply the steady- and ranging-based persistence constructions to toy examples and real-world applications.
Cite
@article{arxiv.2009.06897,
title = {Steady and ranging sets in graph persistence},
author = {Mattia G. Bergomi and Massimo Ferri and Antonella Tavaglione},
journal= {arXiv preprint arXiv:2009.06897},
year = {2022}
}