Generalized Clustering Coefficients and Milgram Condition for q-th Degrees of Separation

Abstract

We introduce a series of generalized clustering coefficients based on String formalism given by Aoyama, using adjacent matrix in networks. We numerically evaluate Milgram condition proposed in order to explore q-th degrees of separation in scale free networks and small world networks. We find that scale free network with exponent 3 just shows 6-degrees of separation. Moreover we find some relations between separation numbers and generalized clustering coefficient in both networks.