Homology of Digraphs
Alexander Asaturovich Grigor'yan, Yu. V. Muranov, Rolando Jiménez · Mathematical Notes · 2021
Abstract 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.