  We present a novel technique for calculating the two-point autocorrelation
function of the Lyman-alpha forest based on the relation between the two-point
correlation function and the Neighbor Probability Distribution Functions. The
technique appears to reduce the scatter in estimates of the correlation
function by a factor of about two from the traditional pair-counting method. We
apply the technique to the Lyman-alpha forest line lists determined from the
spectra of seven z > 2 QSOs observed at high resolution ( < 25 km/s ). Of
these, only two spectra, those of Q0055-259 and Q0014+813, appear to be
sufficiently free of systematics to obtain meaningful estimates of the
correlation function. We find positive correlations, with a maximum amplitude
of 0.5 - 1, on the scale of 0.5 - 3 h^{-1} Mpc (comoving), or 100 - 600 km/s,
in the forests of both QSOs. The technique also finds strong evidence for
anticorrelation on the scale of 3 - 6 h^{-1} Mpc. The strength of the positive
correlations is comparable to that predicted from the primordial power spectrum
inferred from optically-selected galaxy redshift surveys. If the
anticorrelations are physical, it becomes unclear whether the detected
clustering is consistent with current models of structure formation with a
homogeneous photoionizing UV metagalactic background. Instead, the
anti-clustering may require inhomogeneity in the UV background, and possibly in
the process of reionization itself.
