  Multipath cohomology is a cohomology theory for directed graphs, which is
defined using the path poset. The aim of this paper is to investigate
combinatorial properties of path posets, and to provide computational tools for
multipath cohomology. In particular, we develop acyclicity criteria, and
provide computations of multipath cohomology groups of oriented linear graphs.
We further interpret the path poset as the face poset of a simplicial complex,
and we investigate realisability problems.
