  The cluster correlation function and its richness dependence are determined
from 1108 clusters of galaxies -- the largest sample of clusters studied so far
-- found in 379 deg^2 of Sloan Digital Sky Survey early data. The results are
compared with previous samples of optically and X-ray selected clusters. The
richness-dependent correlation function increases monotonically from an average
correlation scale of ~ 12 h^{-1} Mpc for poor clusters to ~ 25 h^{-1} Mpc for
the richer, more massive clusters with a mean separation of ~ 90 h^{-1} Mpc.
X-ray selected clusters suggest slightly stronger correlations than optically
selected clusters (~ 2-\sigma). The results are compared with large-scale
cosmological simulations. The observed richness-dependent cluster correlation
function is well represented by the standard flat LCDM model (\Omega_m ~= 0.3,
h ~= 0.7), and is inconsistent with the considerably weaker correlations
predicted by \Omega_m = 1 models. An analytic relation for the correlation
scale versus cluster mean separation, r_0 - d, that best describes the
observations and the LCDM prediction is r_0 ~= 2.6 \sqrt{d} (for d ~= 20 - 90
h^{-1} Mpc). Data from the complete Sloan Digital Sky Survey, when available,
will greatly enhance the accuracy of the results and allow a more precise
determination of cosmological parameters.
