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A bipartite \( r \)-digraph is an orientation of a bipartite multigraph that is without loops and contains at most \( r \) edges between any pair of vertices from distinct parts. In this paper, we obtain necessary and sufficient conditions for a pair of sequences of non-negative integers in non-decreasing order to be a pair of sequences of numbers, called marks (or \( r \)-scores), attached to the vertices of a bipartite \( r \)-digraph. These characterizations provide algorithms for constructing the corresponding bipartite multi-digraph.