The cellular homology of digraphs
Abstract
In [15], we investigate the pair ($P$, Supp($P$)) of minimal path $P$ and its supporting sub-digraph Supp($P$) in the path complex of a digraph $G$ under the strongly regular condition. In this paper, first, we consider the special minimal path $P$ specified by the admissible condition (Definition 3.8), which means that ($P$, Supp($P$)) admits a singular cubical realization. Based on such a subset, we systematically introduce the definitions of cellular chain complex associated to $G$ and prove the well-definedness. Then we study several properties of such cellular homologies. Finally, we present several intriguing examples as well as some important observations.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Digital Image Processing Techniques
Advanced Topology and Set Theory
Publication details
- Journal / source
- Asian Journal of Mathematics
- Publisher
- International Press of Boston
- Volume
- 30
- Issue
- 1
- Pages
- 61–114
- Publication date
- 1 January 2026
- Language
- EN