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A graph in van Eck and Waltman [JASIST, 60(8), 2009, p. 1644], representing the relation between the association strength and the cosine, is partially explained as a sheaf of parabolas, each parabola being the functional relation between these similarity measures on the trajectories $\vec {X} \cdot \vec {Y} = a$, a constant. Based on earlier obtained relations between cosine and other similarity measures (e.g., Jaccard index), we can prove new relations between the association strength and these other measures. © 2010 Wiley Periodicals, Inc.