Beyond Six Degrees of Separation: Exploring Milgram's Condition in Complex Networks

The concept of six degrees of separation stands as a significant phenomenon, positing that any two independent entities worldwide can connect through a chain of no more than six acquaintances. This article delves into the study of this phenomenon across various network models, aiming to quantify the rates of information propagation, idea dissemination, disease transmission, and predictive trends in society and economics. We extend the examination beyond the conventional notion of "six degrees of separation" by investigating the factors impacting degrees of separation and Milgram's condition in complex networks. Our objective is to elucidate that the actual degree of separation within a network is intricately tied to its structure and various parameters. Instead of being a universal rule, this concept can be construed as a condition that networks must satisfy. We explore Milgram's condition in diverse network models, encompassing random, small-world, and scale-free networks, while scrutinizing the impact of the frequency and length of cycles on degrees of separation. We introduce a novel criterion, termed multiplicity within the network and assess its relationship with the Hamming distance. We evaluate the effectiveness of Milgram's condition and degrees of separation in the context of these two parameters. Our findings underscore the close association between Milgram's condition and degrees of separation with the specific network model and its structure.

Keywords:

Milgram’s Condition , Six Degrees of Separation , Small-Worldness , Hamming Distance , Network Multiplicity , Complex Networks , Graph theory