We introduce a persistent Hochschild homology framework for directed graphs.
Hochschild homology groups of (path algebras of) directed graphs vanish in
degree i≥2. To extend them to higher degrees, we introduce the notion of
connectivity digraphs and analyse two main examples; the first, arising from
Atkin's q-connectivity, and the second, here called n-path digraphs,
generalising the classical notion of line graphs. Based on a categorical
setting for persistent homology, we propose a stable pipeline for computing
persistent Hochschild homology groups. This pipeline is also amenable to other
homology theories; for this reason, we complement our work with a survey on
homology theories of digraphs.Comment: Comments are welcome