  In [16], we observed the graph W*-probability theory. In this paper, we will
review [16] and introduce special amalgamated random variables in this
amalgamated W*-probability space. In particular, we will observe the
amalgamated semicircularity, amalgamated evenness and amalgamated
R-diagonality. As an example, we will compute the trivial moments and trivial
cumulants of the generating operator of the graph W*-algebra.
