Homologies of path complexes and digraphs
By Alexander Grigorʼyan, Yong Lin, Yuri V. Muranov, Shing-Tung Yau. 2012
128 citations recorded by the source corpus.
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 from directed graphs(digraphs). We obtain a new notion of the path homology and cohomology of a digraph.
View Paper: https://www.semanticscholar.org/paper/bc83eaf878acf6450cefed7a69be9c9e4eda348b
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Citations in the corpus
- Homotopy theory for digraphs (2014, methodology): “In Section 2 we give a short survey on homology theory for digraphs following [5], [7].”
- Homologies of digraphs and Künneth formulas (2017, methodology): “We use the notion of path homology of digraphs that was introduced in [9] and [10].”
- Graphs associated with simplicial complexes (2014, methodology): “A dual notion of homology of digraphs based on the notion of path complex was introduced in [7], where the first methods for computing the cohomology groups were developed.”