Comments on Six Degrees of Separation based on the le Pool and Kochen Models

TL;DR

This paper revisits the six degrees of separation concept through numerical analysis of Pool and Kochen's models, incorporating modern network metrics like clustering coefficient to deepen understanding.

Contribution

It provides a numerical study of Pool and Kochen's models using computer simulations and extends analysis with a new method for estimating clustering coefficients.

Findings

Numerical analysis of Pool and Kochen's models conducted.

Clustering coefficient estimated using a novel method.

Extended analysis linking Pool and Kochen's models with modern network metrics.

Abstract

In this article we discuss six degrees of separation, which has been suggested by Milgram's famous experiment\cite{Milg},\cite{Milg2}, from a theoretical point of view again. Though Milgram's experiment was partly inspired to Pool and Kochen's study \cite{Pool} that was made from a theoretical point of view. At the time numerically detailed study could not be made because computers and important concepts, such as the clustering coefficient, needed for a network analysis nowadays, have not yet developed. In this article we devote deep study to the six degrees of separation based on some models proposed by Pool and Kochen by using a computer, numerically. Moreover we estimate the clustering coefficient along the method developed by us \cite{Toyota1} and extend our analysis of the subject through marrying Pool and Kochen's models to our method.