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

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.