  We reformulated the string formalism given by Aoyama, using an adjacent
matrix of a network and introduced a series of generalized clustering
coefficients based on it. Furthermore we numerically evaluated Milgram
condition proposed by their article in order to explore $q$-$th$ degrees of
separation in scale free networks. In this article, we apply the reformulation
to small world networks and numerically evaluate Milgram condition, especially
the separation number of small world networks and its relation to cycle
structures are discussed. Considering the number of non-zero elements of an
adjacent matrix, the average path length and Milgram condition, we show that
the formalism proposed by us is effective to analyze the six degrees of
separation, especially effective for analyzing the relation between the
separation number and cycle structures in a network.
  By this analysis of small world networks, it proves that a sort of power low
holds between $M_n$, which is a key quantity in Milgram condition, and the
generalized clustering coefficients. This property in small world networks
stands in contrast to that of scale free networks.
