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 . 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 . Here we consider the data on the declared number of friends, as collected from  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 . 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 . Analogy with the Benford’s law  is explored. Our analysis could be placed in NSN (new science of network) paradigm .
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