  Given a data-set of consumer behaviour, the Revealed Preference Graph
succinctly encodes inferred relative preferences between observed outcomes as a
directed graph. Not all graphs can be constructed as revealed preference graphs
when the market dimension is fixed. This paper solves the open problem of
determining exactly which graphs are attainable as revealed preference graphs
in $d$-dimensional markets. This is achieved via an exact characterization
which closely ties the feasibility of the graph to the Matrix Sign Rank of its
signed adjacency matrix. The paper also shows that when the preference
relations form a partially ordered set with order-dimension $k$, the graph is
attainable as a revealed preference graph in a $k$-dimensional market.
