A Static Model for Stylized Facts in Social Networks

Jo, Hang-Hyun; Murase, Yohsuke; Török, János; Kertész, János; Kaski, Kimmo
The past analyses of available datasets for social networks have given rise to a number of empirical findings that cover only some parts or aspects of the society, but leave the structure of the whole social network largely unexplored due to lack of even more comprehensive datasets. In order to model the whole social network, we assume that some properties of the network are reflected in empirical findings that are commonly featured as $\backslash$emph{\{}stylized facts{\}} of social networks, such as broad distributions of network quantities, existence of communities, assortative mixing, and intensity-topology correlations. Several models have been studied to generate the stylized facts, but most of them focus on the processes or mechanisms behind stylized facts. In this paper, we take an alternative approach by devising a static model for the whole social network, for which we randomly assign a number of communities to a given set of isolated nodes using a few assumptions, i.e., the community size is heterogeneous, and larger communities are assigned with smaller link density and smaller characteristic link weight. With these assumptions, we are able to generate realistic social networks that show most stylized facts for a wide range of parameters. This in turn can explain why the stylized facts are so commonly observed. We also obtain analytic results for various network quantities that turn out to be comparable with the numerical results. In contrast to the dynamical generative models, our static model is simple to implement and easily scalable. Hence, it can be used as a reference system for further applications.
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