Eur. Phys. J. B 84, 147-159 (2011)
https://doi.org/10.1140/epjb/e2011-20172-4

Regular Article

Communication activity in social networks: growth and correlations

¹ Levich Institute and Physics Department, City College of New York, New York, NY 10031, USA
² Potsdam Institute for Climate Impact Research (PIK), P.O. Box 60 12 03, 14412 Potsdam, Germany
³ Department of Physics, Yeshiva University, New York, NY 10033, USA
⁴ Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
⁵ Department of Sociology, Stockholm University, 10691 Stockholm, Sweden

^a e-mail: ca-dr@rybski.de

Received: 8 March 2011
Received in final form: 2 August 2011
Published online: 26 October 2011

Abstract

We investigate the timing of messages sent in two online communities with respect to growth fluctuations and long-term correlations. We find that the timing of sending and receiving messages comprises pronounced long-term persistence. Considering the activity of the community members as growing entities, i.e. the cumulative number of messages sent (or received) by the individuals, we identify non-trivial scaling in the growth fluctuations which we relate to the long-term correlations. We find a connection between the scaling exponents of the growth and the long-term correlations which is supported by numerical simulations based on peaks over threshold. In addition, we find that the activity on directed links between pairs of members exhibits long-term correlations, indicating that communication activity with the most liked partners may be responsible for the long-term persistence in the timing of messages. Finally, we show that the number of messages, M, and the number of communication partners, K, of the individual members are correlated following a power-law, K ~ M^λ, with exponent λ ≈ 3 / 4.