2018/08/22 by Jesús F. Espinoza, Espinoza, Jesus F., Martín-Eduardo Frias-Armenta +3
Computer Science · Psychology · #05C25 #05C85 #55U05 #55U15 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #K-Theory and Homology (math.KT) #Psychedelics and Drug Studies #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1808.07461
openalex publication_date 2018/08/22 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
The family of \mathfrakI-contractible graphs and contractible transformations was defined by A. Ivashchenko in the mid-90's. In this paper we study the collapsibility and homological properties of the clique complex associated to \mathfrakI-contractible graphs. We show that for any graph in a special subfamily of the \mathfrakI-contractible graphs (the strong \mathfrakI-contractible ones) its clique complex is collapsible. Moreover, we present an algorithm that allows us to verify if any graph is strong \mathfrakI-contractible, as well as an algorithm to delete those vertices whose open neighborhood is also strong \mathfrakI-contractible. Finally, we show how to use these algorithms to compute the persistent homology of an arbitrary Vietoris-Rips complex for applications in topological data analysis.