  In this paper we study the behavior of energy centroids (denoted as
$\bar{E_I}$) of spin $I$ states in the presence of random two-body
interactions, for systems ranging from very simple systems (e.g. single-$j$
shell for very small $j$) to very complicated systems (e.g., many-$j$ shells
with different parities and with isospin degree of freedom). Regularities of
$\bar{E_I}$'s discussed in terms of the so-called geometric chaoticity (or
quasi-randomness of two-body coefficients of fractional parentage) in earlier
works are found to hold even for very simple systems in which one cannot assume
the geometric chaoticity. It is shown that the inclusion of isospin and parity
does not "break" the regularities of $\bar{E_I}$'s.
