Zhao and Karypis (2001) define Purity and Entropy as follows: where q is the number of classes, k the number of clusters, n r cluster r's size, and n i r is the number of elements in class i assigned to cluster r. Both measures are good measures for homogeneity (Purity increases and Entropy decreases when homogeneity increases).
as noted in (Rosenberg and Hirschberg, 2007), these measures evaluate not only the quality of the proposed clustering but also of the mapping scheme.