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].

[1] R. I. M. Dunbar, The social brain hypothesis, Evolutionary Anthropology 6, 178

(1998).

[2] R. I. M. Dunbar, The Social Brain Hypothesis and Human Evolution, Oxford

Research Encyclopedia of Psychology,Mar. 2016.

[3] R. Toivonen, L. Kovanen, M. Kivelä, J.-P. Onnela, J. Saramäki and K. Kaski, A

comparative study of social network models: Network evolution models and nodal

attribute models,Social Networks 31, 240 (2009)

[4] T. Hogg and G. Szabo, Dynamics and diversity of online community activities, EPL

86, 38003 (2009)

[5] J. Kunegis, KONECT: The Koblenz Network Collection. Proceedings of the 22Nd

International Conference on World Wide Web Companion, 1343–1350 (International

World Wide Web Conferences Steering Committee, Switzerland, 2013).

[6] Diagnoza społeczna: zintegrowana baza danych. www.diagnoza.com (in Polish)

[2.03.2017]

[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.

[8] T. Verguts and F. van Opstal, Dissociation of the distance effect and size effect in

one-digit numbers, Psychonomic Bulletin & Review 12, 925 (2005)

[9] J. Golbeck, Benford’s law applies to online social networks, PLoS ONE 10(8):

e0135169 (2015)

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

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