Differential calculus on discrete sets is developed in the spirit of noncommutative geometry.
Any differential algebra on a discrete set can be regarded as a ''reduction''of the ''universal …

In this paper we introduce a path complex that can be regarded as a generalization of the
notion of a simplicial complex. The main motivation for considering path complexes comes …

arXiv:hep-th/9506171v2 26 Jan 1996 Page 1 arXiv:hep-th/9506171v2 26 Jan 1996 June 8th
1995 hep-th/9506171 PEG-06-95 The Small Scale Structure of Space-Time: A Bibliographical …

We construct a cohomology theory on a category of finite digraphs (directed graphs), which
is based on the universal calculus on the algebra of functions on the vertices of the digraph …

We establish a new theory which unifies various aspects of topological approaches for data
science, by being applicable both to point cloud data and to graph data, including networks …

Homologies of digraphs and Künneth formulas Page 1 Communications in Analysis and
Geometry Volume 25, Number 5, 969–1018, 2017 Homologies of digraphs and Künneth …

We introduce the notions of a path complex and its homologies. Particular cases of path
homologies are simplicial homologies and digraph homologies. We state and prove some …

The cohomology of digraphs was introduced for the first time by Dimakis and Müller-
Hoissen. Their algebraic definition is based on a differential calculus on an algebra of …

We construct a new homology theory for the categories of quivers and multigraphs and
describe the basic properties of introduced homology groups. We introduce a conception of …

In the paper we continue the investigation of the path homology theory of digraphs that was
constructed in our previous papers. We prove basic theorems that are similar to the …