Entropy Production in Stationary Social Networks

The journal article "On the computation of entropy production in stationary social networks" by Tobias Hoßfeld, Valentin Burger, Haye Hinrichsen, Matthias Hirth, Phuoc Tran-Gia has been published  in Springer's Social Network Analysis and Mining, Vol. 4, Issue 1, April 2014.  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 online social networks. As major contribution, we show the relation and difference between entropy production and existing metrics. The comparison shows that computational intensive metrics like centrality can be approximated by entropy production for typical online social networks. To compute the entropy production from real-world measurements, the need for Bayesian inference and the limits of naïve estimates for those probability currents are shown. As further contribution, a general scheme is presented to measure the entropy production in small-world networks using Bayesian inference. The scheme is then applied for a specific example of the R mailing list. Entropy production can be used for communication networks or interaction graphs in general, but it can also be applied for a variety of di.fferent purposes like anomaly detection, leader and spammer detection in communication and social networks, or characterization of traffic flows in the Internet. Paper: Download the full paper in PDF format from the author's website or http://dx.doi.org/10.1007/s13278-014-0190-8.