Abstract: We have been witnessing in the last years a growing interest in new features associated to (directed) graphs. The aim of the talk is to describe the construction of a recently developed (co)homology theory of directed graphs, called multipath cohomology, in terms of a suitable homology theory of posets. Then, we will describe the relations with further homology theories of algebras, e.g. Hochschild and symmetric homology. Depending on the time, we will also present some recent (qualitative and quantitative) results on the homotopy-type of multipath complexes. This is joint work with C. Collari, S. Di Trani, and J. P. Smith.