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Milgram Condition proposed by Aoyama et al. plays an important role on theanalysis of "six degrees of separation". We have shown that the relationsbetween Milgram condition and the generalized clustering coefficient, which wasintroduced as an index for measuring the number of closed paths by us, areabsolutely different in scale free networks (Barabasi and Albert) and smallworld networks (Watts and Strogatz, Watts). This fact implies that the effectof closed paths on information propagation is different in both networks. Inthis article, we first investigate the difference and pursuit what is a crucialmathematical quantity for information propagation. As a result we find that asort of "disorder" plays more important role for information propagation thanpartially closed paths included in a network. Next we inquired into it in moredetail by introducing two types of intermediate networks. Then we find that theaverage of the local clustering coefficient and the generalized clusteringcoefficients $C_{(q)}$ have some different functions and important meanings,respectively. We also find that $C_{(q)}$ is close to the propagation ofinformation on networks. Lastly, we show that realizability of six degrees ofseparation in networks can be understood in a unified way by disorder.

Effect of Closed Paths in Complex networks on Six Degrees of Separation and Disorder