Maria Nawojczyk, Maria Stojkow, Dorota Żuchowska-Skiba, Małgorzata Krawczyk, Krzysztof Kułakowski

The number of acquaintances has been highlighted by Robin Dunbar as a relevant measure of social functions of brain [1,2]. This number is also relevant for modeling social networks [3]. The distribution of the number of social links, as measured in social media, has been reported as a scale-free function [4,5]. On the other hand, the order of magnitude of the mean degree in social networks is often so large that the binning procedure hides details of the distribution [5]. Here we consider the data on the declared number of friends, as collected from [6] for respondents above 50 years. We demonstrate, that the answers on the number of friends show sharp maxima at 10, 15, 20 and sometimes 30, which accompany a broader peak between 0 and 8 [7]. These results do not change qualitatively with sex and age of the respondents. The results are interpreted as a demonstration of the size effect, which applies to the reported values as well as to their uncertainty [8]. Analogy with the Benford’s law [9] is explored. Our analysis could be placed in NSN (new science of network) paradigm [10].

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[7] M. Nawojczyk, M. Stojkow, D. Żuchowska-Skiba, M. J. Krawczyk and K. Kułakowski, Multiples of ten in the survey data on the number of friends, to be published.

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[10] D. Watts, Everything is Obvious: Once You Know the Answers, NY: Crown
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