  For several important classes of manifolds acted on by the torus, the
information about the action can be encoded combinatorially by a regular
n-valent graph with vector labels on its edges, which we refer to as the torus
graph. By analogy with the GKM-graphs, we introduce the notion of equivariant
cohomology of a torus graph, and show that it is isomorphic to the face ring of
the associated simplicial poset. This extends a series of previous results on
the equivariant cohomology of torus manifolds. As a primary combinatorial
application, we show that a simplicial poset is Cohen-Macaulay if its face ring
is Cohen-Macaulay. This completes the algebraic characterisation of
Cohen-Macaulay posets initiated by Stanley. We also study blow-ups of torus
graphs and manifolds from both the algebraic and the topological points of
view.
