Homotopy theory for digraphs

Understand

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers.

• In particular, we prove the homotopy invariance of homologies of digraphs and the relation between the fundamental group of the digraph and its first homology group.
• The category of (undirected) graphs can be identified by a natural way with a full subcategory of digraphs.
• Thus we obtain also consistent homology and homotopy theories for graphs.