Homotopy theory for digraphs

By Alexander Grigorʼyan, Yong Lin, Yuri V. Muranov, Shing-Tung Yau. 2014

134 citations recorded by the source corpus.

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. Note that the homotopy theory for graphs coincides with the one constructed in the paper of Babson et.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/184337219d17c836be1486cc5aed5e81f6324649

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In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homologies of digraphs and Künneth formulas (2017, methodology): “Secondly, there is an independently developed notion of homotopy of digraphs [10] (similar to homotopy theory on graphs [1], [3]) that is compatible with path homology.”