The minimum k-way discrepancy of a rectangular matrix of nonnegative entries is the minimum of the maxima of the within- and between-cluster discrepancies that can be obtained by simultaneous k-clusterings (proper partitions) of its rows and columns. In Theorem 2, irrespective of the size of , we give the following estimate for the kth largest nontrivial singular value of the normalized matrix: , provided and . This statement is a certain converse of Theorem 7 of Bolla (2014), and the proof uses some lemmas and ideas of Butler (2006), where the k=1 case is treated. The result naturally extends to the singular values of the normalized adjacency matrix of a weighted undirected or directed graph.