Infering and Calibrating Triadic Closure in a Dynamic Network
In the social sciences, the hypothesis of triadic closure contends that new links in a social contact network arise preferentially between those who currently share neighbours. Here, in a proof-of-principle study, we show how to calibrate a recently propo
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Abstract In the social sciences, the hypothesis of triadic closure contends that new links in a social contact network arise preferentially between those who currently share neighbours. Here, in a proof-of-principle study, we show how to calibrate a recently proposed evolving network model to time-dependent connectivity data. The probabilistic edge birth rate in the model contains a triadic closure term, so we are also able to assess statistically the evidence for this effect. The approach is shown to work on data generated synthetically from the model. We then apply this methodology to some real, large-scale data that records the build up of connections in a business-related social networking site, and find evidence for triadic closure.
1 Motivation Many modern application areas give rise to patterns of connectivity that change over time [9]. Examples include mobile telecommunication, on-line trading, smartmetering, massive multiplayer online gaming and online social networking. Information such as ‘who called who’, ‘who tweeted who’, ‘who FaceTimed who’, and ‘people who bought his book also bought . . . ’ is naturally evolving over time and cannot be fully exploited through a static representation as a single time-average or snapshot. These emerging, data-rich disciplines generate large, highly-resolved network sequences that demand new models and computational tools. This work focuses on the use of a mathematical model to describe the microscale, transient dynamics. The model, from [5], is mechanistic, incorporating the triadic closure effect that many social scientists believe to be a key driving force behind social interactions. We show how a likelihood approach can be used to calibrate the
A.V. Mantzaris D.J. Higham () Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK e-mail: [email protected]; [email protected] P. Holme and J. Saram¨aki (eds.), Temporal Networks, Understanding Complex Systems, DOI 10.1007/978-3-642-36461-7 13, © Springer-Verlag Berlin Heidelberg 2013
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model, thereby allowing the triadic closure hypothesis to be tested statistically on real data. The manuscript is organised as follows. In Sect. 2 we introduce the triadic closure concept and discuss some relevant work in the area. In Sect. 3 we describe the model from [5] and illustrate its use. Section 4 then explains how the likelihood—the probability of observing the microscale, edge by edge, data given a set of model parameters—can be computed and used to perform statistical inference. To illustrate the idea, we generate synthetic data from the model and reverse engineer the model parameters. In Sect. 5 we then apply these ideas to a set of online social interaction data. Section 6 gives a summary and points to future work.
2 Background The concept of triadic closure can be traced back to the work of the sociologist Georg Simmel in the early 1900s, and was popularized by the influential article [4]. It is a key motivation for the use of clu
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