Dynamics of Social Networks

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Uncovering the complex pattern that stems from the interactions among the members of a society is a complicated task. Societies tend to organize themselves in a modular manner, where the constituent block may be a family, a company, a city, etc. The identification of the dynamical rules of formation of these modules can be a very difficult task, since the definition of these modules depends on the ``scale'' at which the network is analyzed. The researchers intend to introduce a statistical method (the so-called self-similar measure) based on partitioning a complex network with successively larger tiles in order to unravel the modular structure of social networks and study the dependence of these modules on the scale of observation. In this way, they will study whether the dynamical evolution of modules, and then modules of modules and so on, behave in a similar way. It is, also, well known that the multitude of social interactions may create networks with different properties in a society. According to preliminary results, some types of social networks follow this self-similarity in their characteristics, while others do not. The researchers will classify the available social networks according to the self-similarity property and study how modules emerge in a population. The importance of this modularity will then be highlighted in important applications, such as the implications for the efficiency of immunization efforts. This project involves a number of different datasets, gathered through international collaborations, that represent the state-of-the-art in the field, both in terms of size and accuracy. By applying mathematical tools to the social networks studying the described properties, the researchers aim to reach conclusions that will be of mutual interest to sociologists and physicists.