Previous analysis has shown that the sizes of voids determined by members of superclusters of different richness are almost identical. This result, and the absence of a randomly located population of clusters in voids, suggest that practically all clusters are located in void walls, and the overall distribution of superclusters of different richness is rather similar. Now we shall study the distribution of superclusters of different richness in void walls. For that we calculate for each supercluster centre the distances to the centres of three nearest superclusters, separately for poor and medium rich, and for very rich superclusters (Fig. 8 (click here)).
On the upper panel of Fig. 8 (click here) these distributions are given for
poor and medium rich superclusters. We see, first, that these
distances are small, and second, that these distributions are
smooth and do not show the presence of any preferred distance
between superclusters (that would be seen as a peak in the distance
distribution). The median distances to the first, second and third
neighbours are, correspondingly, 
, 
and
75 h
Mpc.
In the case of poor and medium rich superclusters from random
catalogues the median distances to the first,
second and third neighbours are closer to each other than in the
observed case: 
,
and 
h
Mpc.
The distributions of distances between very rich superclusters
(Fig. 8 (click here), lower panel) are quite different. None of these
distributions is smooth as in the upper panel. The most important
feature in this figure is the presence of a peak in the distribution of
distances of the second and third neighbour in the interval 
150 h
Mpc - over 75% of very rich superclusters
have a neighbour at this distance. The median distances to the
second and third neighbours are, correspondingly, 
and 
h
Mpc. These values are close to the size of
voids between superclusters.
Since the number of very rich superclusters is small, it is easy to check to which supercluster pairs these distances correspond. This analysis confirms that the peak in the distribution of the second and third neighbour is due to the pairs of superclusters on opposite sides of void walls.
Also, this analysis shows that about half of the very rich
superclusters have their first nearest very rich neighbour at the
same side of the void (examples of such pairs are the
Fornax-Eridanus and the Caelum superclusters, the superclusters in
the Aquarius complex and others) at a distance less than 
h
Mpc.
One can argue that the last result may simply be due to the small
number of very rich superclusters. Thus we performed the same
analysis with superclusters from random catalogues. In this case
the distributions of neighbour distances for superclusters of all
richnesses are smoothly increasing without any strong peak as in the
observed case for very rich superclusters. The median distances
between centres of randomly located very rich superclusters are:
h
Mpc, 
h
Mpc, and
h
Mpc, values that are much larger than in
the observed case.
This test shows that the overall distribution of superclusters of various richnesses is rather similar, but the distribution of superclusters in void walls depends on the supercluster richness.
Additional evidence for differences in the distribution of poor and rich superclusters comes from the analysis of the correlation function of clusters of galaxies (Einasto et al. 1997b).