Entropy Production in Stationary Social Networks

  • Haye Hinrichsen
  • Tobias Hoßfeld
  • Matthias Hirth
  • Phuoc Tran-Gia
Part of the Studies in Computational Intelligence book series (SCI, volume 476)


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.


Social Network Entropy Production Mailing List Incoming Link Geiger Counter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Jin, E.M., Girvan, M., Newman, M.E.J.: Structure of growing social networks. Phys. Rev. E 64 (September 2001)Google Scholar
  2. 2.
    Barnes, N.G., Andonian, J.: The 2011 fortune 500 and social media adoption: Have america’s largest companies reached a social media plateau? (2011),
  3. 3.
    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)Google Scholar
  4. 4.
    Schnakenberg, J.: Network theory of microscopic and macroscopic behavior of master equation systems. Rev. Mod. Phys. 48 (October 1976)Google Scholar
  5. 5.
    Schreiber, T.: Measuring information transfer. Phys. Rev. Lett. 85 (July 2000)Google Scholar
  6. 6.
    Andrieux, D., Gaspard, P.: Fluctuation theorem and onsager reciprocity relations. J. Chem. Phys. 121(13) (2004)Google Scholar
  7. 7.
    Seifert, U.: Entropy production along a stochastic trajectory and an integral fluctuation theorem. Phys. Rev. Lett. 95 (July 2005)Google Scholar
  8. 8.
    Zeerati, S., Jafarpour, F.H., Hinrichsen, H.: Entropy production of nonequilibrium steady states with irreversible transitions (2012) (under submission) Google Scholar
  9. 9.
    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)Google Scholar
  10. 10.
  11. 11.
    Ebel, H., Mielsch, L.I., Bornholdt, S.: Scale-free topology of e-mail networks. Phys. Rev. E 66 (September 2002)Google Scholar
  12. 12.
    Garrido, A.: Symmetry in complex networks. Symmetry 3(1) (2011)Google Scholar
  13. 13.
    Garrido, A.: Classifying entropy measures. Symmetry 3(3) (2011)Google Scholar
  14. 14.
    Mowshowitz, A., Dehmer, M.: A symmetry index for graphs. Symmetry: Culture and Science 21(4) (2010)Google Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    Bilgin, C., Yener, B.: Dynamic network evolution: Models, clustering, anomaly detection. Technical report, Rensselaer University, NY (2010)Google Scholar
  17. 17.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Haye Hinrichsen
    • 1
  • Tobias Hoßfeld
    • 2
  • Matthias Hirth
    • 2
  • Phuoc Tran-Gia
    • 2
  1. 1.Department of Physics and AstronomyUniversity of WürzburgWürzburgGermany
  2. 2.Institute of Computer Science, Communication NetworksUniversity of WürzburgWürzburgGermany

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