  In previous papers it was demonstrated that lower performance groups have a
larger size-dependent cumulative advantage for receiving citations than
top-performance groups. Furthermore, regardless of performance, larger groups
have less not-cited publications. Particularly for the lower performance groups
the fraction of not-cited publications decreases considerably with size. These
phenomena can be explained with a model in which self-citation acts as a
promotion mechanism for external citations. In this article we show that for
self-citations similar size-dependent scaling rules apply as for citations but
generally the power law exponents are higher for self-citations as compared to
citations. We also find that the fraction of self-citations is smaller for the
higher performance groups and this fraction decreases more rapidly with
increasing journal impact than for lower performance groups. An interesting
novel finding is that the variance in the correlation of the number of
self-citations with size is considerably less than the variance for external
citations. This is a clear indication that size is a stronger determinant for
self-citations than for external citations. Both higher and particularly lower
performance groups have a size-dependent cumulative advantage for
self-citations, but for the higher performance groups only in the lower impact
journals and in fields with low citation density.
