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The mystery of the six degrees of separation, part II: navigability and small worlds

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Lettera Matematica

Abstract

Sometimes the world appears to be as big as we thought. How many times have you met someone for the first time, maybe in another city, and discovered that you have friends in common? Indeed the experience and experiments, such as those of the famous sociologist Milgram in the 1960s, show that in most cases short chains of acquaintances are enough to connect any two people on the planet. This phenomenon became known as the mystery of the “six degrees of separation”, and it is increasingly relevant due to the importance that natural and technological networks have taken today. The aim of this two-part article is to address the issue from mathematical and historical point of view, showing how the graphs are a good tool to analyse the problem. In this second part we treat navigability and small-world networks.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Camerino, Via Madonna delle Carceri, 9, 62032, Camerino, MC, Italy

    Stefano Leonesi

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  1. Stefano Leonesi
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Correspondence to Stefano Leonesi.

Additional information

For the notation, terminology and part I of this paper, see [4].

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Leonesi, S. The mystery of the six degrees of separation, part II: navigability and small worlds. Lett Mat Int 3, 215–220 (2015). https://doi.org/10.1007/s40329-015-0096-y

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  • DOI: https://doi.org/10.1007/s40329-015-0096-y

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