pci(x1, x2)x1 and x2, $n00$ the number of item pairs that occur in differenct clusters in both partitions, $n10$ the number of item pairs that occur in the same cluster in partition x1 but in different clusters in parition x2, and $n01$ the number of item pairs that occur in different clusters in partition x1 but in the same cluster in partition x2. The Rand index is given by $$\frac{n_{11}+n_{00}}{n_{11}+n_{00}+n_{01}+n_{10}}.$$ The Fowlkes and Mallows index is given by $$\frac{n_{11}}{\sqrt{(n_{11}+n_{01})(n_{11}+n_{10})}}.$$ The Wallace indices are respectively given by $$\frac{n_{11}}{n_{11}+n_{10}}\qquad\frac{n_{11}}{n_{11}+n_{01}}.$$ The Jaccard index is given by $$\frac{n_{11}}{n_{11}+n_{01}+n_{10}}.$$
Rand, W. (1971) Objective Criteria for the Evaluation of Clustering Methods. Journal of the American Statistical Association 66:846-850
Fowlkes, E. B. and Mallows, C. L. (1983) A Method for Comparing Two Hierarchical Clusterings. Journal of the American Statistical Association 78:553-569
Wallace, D. L. (1983) A Method for Comparing Two Hierarchical Clusterings: comment. Journal of the American Statistical Association 78:569-576