Homologies of path complexes and digraphs
  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. 
Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau
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