  The phenomenon of six degrees of separation is an old but interesting
problem. The considerations of the clustering coefficient reflecting triangular
structures and its extension to square one to six degrees of separation have
been made\cite{Newm21}. Recently, Aoyama\cite{Aoyama} has given some
considerations to this problem in networks without loops, using a sort of
general formalism, "string formalism". In this article, we describe relations
between the string formulation proposed by Aoyama and an adjacent matrix. Thus
we provided a reformulation of the string formulation proposed by \cite{Aoyama}
to analyze networks. According to it, we introduced a series of generalized
$q$-$th$ clustering coefficients. The available rules between diagrams of
graphs and formulae are also given based on the formulation. Next we apply the
formulation to some subjects in order to mainly check consistency with former
studies. By evaluating the clustering coefficient for typical networks studied
well earlier, we confirm a validity of our formulation. Lastly we applied it to
the subject of two degrees of separation.
