Stability of persistent path homology of path complexes

2026-07-28

AI Summary

This study addresses the stability of persistent path homology on path complexes under perturbations. Building upon path homology theory from algebraic topology and the framework of persistent homology, combined with perturbation analysis in metric spaces, the authors establish the first Lipschitz stability theorem for persistent path homology of path complexes. This result not only unifies and recovers classical stability statements for directed graphs but also extends them to broader discrete structures such as hypergraphs and sequential hypergraphs, thereby providing a rigorous theoretical foundation for topological data analysis on these objects.

Abstract

We show stability of persistent path homology of path complexes. As a consequence, we deduce the stability of persistent path homology of hypergraphs and of sequence hypergraphs, and recover the known stability result for digraphs, originally due to Chowdhury and Mémoli.

Problem

• persistent path homology
• path complexes
• stability
• hypergraphs
• digraphs

Innovation

• persistent path homology
• stability
• path complexes
• hypergraphs
• directed graphs