Overlap coefficient

The overlap coefficient (or, Szymkiewicz-Simpson coefficient) is a similarity measure related to the Jaccard index that measures the overlap between two sets, and is defined as the size of the intersection divided by the smaller of the size of the two sets:

$\mathrm {overlap} (X,Y)={\frac {|X\cap Y|}{\min(|X|,|Y|)}}$

If set X is a subset of Y or the converse then the overlap coefficient is equal to one.