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We have measured the correlation functions of the optically selected clustersof galaxies in the Abell and the APM catalogs, and of the X-ray clusters in theX-ray-Brightest Abell-type Clusters of galaxies (XBACs) catalog and theBrightest Clusters Sample (BCS). The same analysis method and the same methodof characterizing the resulting correlation functions are applied to allobservational samples. We have found that the amplitude of the correlationfunction of the APM clusters is much higher than what has been previouslyclaimed, in particular for richer subsamples. The correlation length of the APMclusters with the richness R >= 70 (as defined by the APM team) is found to ber_0 = 25.4(+3.1,-3.0) h^(-1)Mpc. The amplitude of correlation function is about2.4 times higher than that of Croft et al. (1997). The correlation lengths ofthe Abell clusters with the richness class RC >= 0 and 1 are measured to be r_0= 17.4(+1.2,-1.1) and 21.0(+2.8,-2.8) h^(-1)Mpc, respectively, which isconsistent with our results for the APM sample at the similar level ofrichness. The richness dependence of cluster correlations is found to be r_0 =0.40*d_c + 3.2 where d_c is the mean intercluster separation. This is identicalin slope with the Bahcall & West (1992)'s estimate, but is inconsistent withthe weak dependence of Croft et al. (1997). The X-ray bright Abell clusters inthe XBACs catalog and the X-ray selected clusters in the BCS catalog showstrong clustering. The correlation length of the XBACs clusters with L_x >=0.65*10^44 h^(-2)erg/s is 30.3(+8.2,-6.5) h^(-1)Mpc, and that of the BCSclusters with L_x >= 0.70*10^44 h^(-2)erg/s is 30.2(+9.8,-8.9) h^(-1)Mpc. Theclustering strength of the X-ray clusters is much weaker than what is expectedfrom the optical clusters.Comment: 10 pages, 4 figures, references for more recent works are adde

CORRELATION FUNCTIONS OF THE ABELL, APM, AND X-RAY CLUSTERS OF GALAXIES