We analyse the spatial clustering properties of a new catalogue of very rich galaxy clusters selected from the APM Galaxy Survey .
These clusters are of comparable richness and space density to Abell Richness Class \geq 1 clusters , but selected using an objective algorithm from a catalogue demonstrably free of artificial inhomogeneities .
Evaluation of the two-point correlation function \xi _ { cc } ( r ) for the full sample and for richer subsamples reveals that the correlation amplitude is consistent with that measured for lower richness APM clusters and X-ray selected clusters .
We apply a maxmimum likelihood estimator to find the best fitting slope and amplitude of a power law fit to \xi _ { cc } ( r ) , and to estimate the correlation length r _ { 0 } ( the value of r at which \xi _ { cc } ( r ) is equal to unity ) .
For clusters with a mean space density of 1.6 \times 10 ^ { -6 } h ^ { 3 } { Mpc } ^ { -3 } ( equivalent to the space density of Abell Richness \geq 2 clusters ) , we find r _ { 0 } = 21.3 ^ { +11.1 } _ { -9.3 } h ^ { -1 } { Mpc } ( 95 \% confidence limits ) .
This is consistent with the weak richness dependence of \xi _ { cc } ( r ) expected in Gaussian models of structure formation .
In particular , the amplitude of \xi _ { cc } ( r ) at all richnesses matches that of \xi _ { cc } ( r ) for clusters selected in N-Body simulations of a low density Cold Dark Matter model .