Martin-Luther-Universität Halle-Wittenberg


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About growth and correlations in cities and social communities

Diego Rybski

(Potsdam-Institut für Klimafolgenforschung, Potsdam)


Growth processes are common in nature, society, and technology. Recently, non-trivial scaling relations have been found in the growth of companies, i.e. both, the average growth rate and the conditional standard deviation, decay as power-laws with the size of the companies. These findings contradict Gibrat's law, which has been postulated to explain broad size distributions, such as of companies, and which assumes growth rates that are independent of the size of the entities. Here, the growth in two different fields is investigated -- both exhibiting characteristic growth patterns: (i) We analyze population data and apply a new method in order to identify population agglomerations based on spatial distributions beyond administrative boundaries. The obtained scaling relations are due to an underlying correlated process. (ii) Millions of messages sent in two social online communities are analyzed by considering the cumulative number of messages sent by each member as growing entity. We identify similar scaling laws in the growth rates and attribute them to a long-term persistence of human activity beyond daily or weekly cycles holding up to more than a year.

[1] H.D. Rozenfeld, D. Rybski et al., Laws of population growth,
PNAS 105, 18702 (2008).
[2] D. Rybski et al., Scaling laws of human interaction activity, PNAS 106, 12640 (2009).

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