Homology of Digraphs

Grigoryan A, Muranov YV, Jimenez R. Homology of Digraphs. Mathematical Notes volume. 2021;109(5-6):712-726.A theory of singular cubic homology of digraphs is developed; the obtained homology groups are proved to be functorial and homotopy invariant. Commutative diagrams of exact sequences similar to the classical ones are constructed, and a relationship between the cubic homology and the path homology of a digraph is described. Carrying over the results to graphs, multigraphs, and quivers is discussed