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

TL;DR

This paper introduces generalized clustering coefficients using String formalism and evaluates the Milgram condition to analyze degrees of separation in scale-free and small-world networks, revealing key relationships and specific separation degrees.

Contribution

It presents new generalized clustering coefficients based on String formalism and applies them to explore degrees of separation in different network models.

Findings

Scale-free network with exponent 3 shows 6-degrees of separation.

Relations found between separation numbers and clustering coefficients.

Milgram condition effectively evaluates 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.