Homologies of path complexes and digraphs

Alexander Grigor'yan Yong Lin Yuri Muranov Shing-Tung Yau

Algebraic Topology and General Topology mathscidoc:1912.43585

arXiv preprint arXiv:1207.2834, 2012.7
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.
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  title={Homologies of path complexes and digraphs},
  author={Alexander Grigor'yan, Yong Lin, Yuri Muranov, and Shing-Tung Yau},
  booktitle={arXiv preprint arXiv:1207.2834},
Alexander Grigor'yan, Yong Lin, Yuri Muranov, and Shing-Tung Yau. Homologies of path complexes and digraphs. 2012. In arXiv preprint arXiv:1207.2834. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204235770847149.
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