Abstract
Completing their initial phase of rapid growth social networks are expected to reach a plateau from where on they are in a statistically stationary state. Such stationary conditions may have different dynamical properties. For example, if each message in a network is followed by a reply in opposite direction, the dynamics is locally balanced. Otherwise, if messages are ignored or forwarded to a different user, one may reach a stationary state with a directed flow of information. To distinguish between the two situations, we propose a quantity called entropy production that was introduced in statistical physics as a measure for non-vanishing probability currents in nonequilibrium stationary states. The proposed quantity closes a gap for characterizing social networks. As major contribution, we present a general scheme that allows one to measure the entropy production in arbitrary social networks in which individuals are interacting with each other, e.g. by exchanging messages. The scheme is then applied for a specific example of the R mailing list.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Jin, E.M., Girvan, M., Newman, M.E.J.: Structure of growing social networks. Phys. Rev. E 64 (September 2001)
Barnes, N.G., Andonian, J.: The 2011 fortune 500 and social media adoption: Have america’s largest companies reached a social media plateau? (2011), http://www.umassd.edu/cmr/socialmedia/2011fortune500/
Hoßfeld, T., Hirth, M., Tran-Gia, P.: Modeling of Crowdsourcing Platforms and Granularity of Work Organization in Future Internet. In: International Teletraffic Congress (ITC), San Francisco, USA (September 2011)
Schnakenberg, J.: Network theory of microscopic and macroscopic behavior of master equation systems. Rev. Mod. Phys. 48 (October 1976)
Schreiber, T.: Measuring information transfer. Phys. Rev. Lett. 85 (July 2000)
Andrieux, D., Gaspard, P.: Fluctuation theorem and onsager reciprocity relations. J. Chem. Phys. 121(13) (2004)
Seifert, U.: Entropy production along a stochastic trajectory and an integral fluctuation theorem. Phys. Rev. Lett. 95 (July 2005)
Zeerati, S., Jafarpour, F.H., Hinrichsen, H.: Entropy production of nonequilibrium steady states with irreversible transitions (2012) (under submission)
Box, G.E.P., Tiao, G.C.: Bayesian Inference in Statistical Analysis. John Wiley & Sons, New York (1973); (reprinted in paperback 1992 ISBN: 0-471-57428-7 pbk)
R Mailing Lists, http://tolstoy.newcastle.edu.au/R/
Ebel, H., Mielsch, L.I., Bornholdt, S.: Scale-free topology of e-mail networks. Phys. Rev. E 66 (September 2002)
Garrido, A.: Symmetry in complex networks. Symmetry 3(1) (2011)
Garrido, A.: Classifying entropy measures. Symmetry 3(3) (2011)
Mowshowitz, A., Dehmer, M.: A symmetry index for graphs. Symmetry: Culture and Science 21(4) (2010)
Xiao, Y.H., Wu, W.T., Wang, H., Xiong, M., Wang, W.: Symmetry-based structure entropy of complex networks. Physica A: Statistical Mechanics and its Applications 387(11) (2008)
Bilgin, C., Yener, B.: Dynamic network evolution: Models, clustering, anomaly detection. Technical report, Rensselaer University, NY (2010)
Hoßfeld, T., Lehrieder, F., Hock, D., Oechsner, S., Despotovic, Z., Kellerer, W., Michel, M.: Characterization of BitTorrent Swarms and their Distribution in the Internet. Computer Networks 55(5) (April 2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hinrichsen, H., Hoßfeld, T., Hirth, M., Tran-Gia, P. (2013). Entropy Production in Stationary Social Networks. In: Ghoshal, G., Poncela-Casasnovas, J., Tolksdorf, R. (eds) Complex Networks IV. Studies in Computational Intelligence, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36844-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-36844-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36843-1
Online ISBN: 978-3-642-36844-8
eBook Packages: EngineeringEngineering (R0)