Distance-dependent connectivity: Yet Another Approach to the Small World Phenomenon

Details Distance-dependent connectivity: Yet Another Approach to the Small World Phenomenon Distance-dependent connectivity: Yet Another Approach to the Small World Phenomenon

2005-03-17

arxiv.org/abs/physics/0503148v3

Physica A, 360/2, 617-628 (2006)

Physics

Physics and Society

14 pages, 6 Metapost figures, LaTeX; minor changes (e.g. Fig. 1) and corrected typos

Scientific paper

10.1016/j.physa.2005.06.038

We investigate a relationship network of humans located in a metric space where relationships are drawn according to a distance-dependent probability density. The obtained spatial graph allows us to calculate the average separation of people in a very simple manner. The acquired results agree with the well-known presence of the small-world phenomenon in human relationships. They indicate that this feature can be understood merely as a consequence of the probability composition. We also examine how this phenomenon evolves with the development of human society.

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