Models, Entropy and Information of Temporal Social Networks
Temporal social networks are characterized by heterogeneous duration of contacts, which can either follow a power-law distribution, such as in face-to-face interactions, or a Weibull distribution, such as in mobile-phone communication. Here we model the d
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Abstract Temporal social networks are characterized by heterogeneous duration of contacts, which can either follow a power-law distribution, such as in face-to-face interactions, or a Weibull distribution, such as in mobile-phone communication. Here we model the dynamics of face-to-face interaction and mobile phone communication by a reinforcement dynamics, which explains the data observed in these different types of social interactions. We quantify the information encoded in the dynamics of these networks by the entropy of temporal networks. Finally, we show evidence that human dynamics is able to modulate the information present in social network dynamics when it follows circadian rhythms and when it is interfacing with a new technology such as the mobile-phone communication technology.
1 Introduction The theory of complex networks [1–6] has flourished thanks to the availability of new datasets on large complex systems, such as the Internet or the interaction networks inside the cell. In the last 10 years attention has been focusing mainly on static or growing complex networks, with little emphasis on the rewiring of the links. The topology of these networks and their modular structure [7–10] are able to affect the dynamics taking place on them [5, 6, 11, 12]. Only recently temporal
K. Zhao Physics Department, Northeastern University, Boston, 02115 MA, USA e-mail: [email protected]; M. Karsai BECS, School of Science, Aalto University, Aalto, Finland e-mail: [email protected] G. Bianconi () School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK e-mail: [email protected] P. Holme and J. Saram¨aki (eds.), Temporal Networks, Understanding Complex Systems, DOI 10.1007/978-3-642-36461-7 5, © Springer-Verlag Berlin Heidelberg 2013
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networks [13–18], dominated by the dynamics of rewirings, are starting to attract the attention of quantitative scientists working on complexity. One of the most beautiful examples of temporal networks are social interaction networks. Indeed, social networks [19, 20] are intrinsically dynamical and social interactions are continuously formed and dissolved. Recently we are gaining new insights into the structure and dynamics of these temporal social networks, thanks to the availability of a new generation of datasets recording the social interactions of the fast time scale. In fact, on one side we have data on face-to-face interactions coming from mobile user devices technology [21,22], or Radio-Frequency-Identification-Devices [16, 17], on the other side, we have extensive datasets on mobile-phone calls [23] and agent mobility [24, 25]. This new generation of data has changed drastically the way we look at social networks. In fact, the adaptability of social networks is well known and several models have been suggested for the dynamical formation of social ties and the emergence of connected societies [26–29]. Nevertheless, the strength and nature of a social tie remained difficult to quantify for several years despit
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