Currently, there is no way to set weight to Homogeneity and Completeness when calculating the V-Measure score.

As the paper states (A. Rosenberg, ‎2007), so as the F1-Score is to Precision and Recall, V-Measure score is the harmonic mean of Homogeneity and Completeness. However, we have the function fbeta_score to calculate the Fb-Score, but (as far as I know) we do not have a way of calculating a weighted V-Measure score.

Options:
Add beta=1 parameter to v_measure_score function, where beta < 1 renders more weight to Homogeneity, while beta > 1 gives more weight to Completeness.
Add new function v_beta_measure_score in order to keep it separated from the original function, just as fbeta_score is separated from f1_score