Homologies of path complexes and digraphs

12 Jul 2012 · Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau ·

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.