Eur. Phys. J. B 76, 87-97 (2010)
https://doi.org/10.1140/epjb/e2010-00216-1

Unravelling the size distribution of social groups with information theory in complex networks

¹ Departament ECM, Facultat de Física, Universitat de Barcelona. Diagonal 647, 08028 Barcelona, Spain
² Departament FFN, Facultat de Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
³ Sogeti España, WTCAP 2, Plaça de la Pau s/n, 08940 Cornellà, Spain
⁴ National University La Plata, IFCP-CCT-CONICET, C.C. 727, 1900 La Plata, Argentina

Corresponding authors: ^a alberto@ecm.ub.es - ^b plastino@fisica.unlp.edu.ar

Received: 12 September 2009
Revised: 17 February 2010
Published online: 2 July 2010

Abstract

The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E 60, 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [Phys. A 389, 490 (2010)]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place, for a competitive cluster growth process, in a scale-free ideal network – a non-correlated network with a connection-degree's distribution that mimics the scale-free ideal gas density distribution. We use a scaling rule that allows one to classify the final cluster-size distributions using only one parameter that we call the competitiveness, which can be seen as a measure of the strength of the interactions. We find that both empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness-parameter, that also allow us to infer the maximum number of stable social relationships that one person can maintain, known as the Dunbar number, together with its standard deviation. We discuss the importance of this number in connection with the empirical phenomenon known as “six-degrees of separation”. Finally, we show that scaled city-size distributions of large countries follow, in general, the same universal distribution.