Dynamics of Social Networks

揭示一个社会成员之间互动的复杂模式是一项复杂的任务。社会倾向于以模块化的方式组织自己，其中的组成块可能是一个家庭，一个公司，一个城市等，这些模块的形成的动态规则的识别可能是一项非常困难的任务，因为这些模块的定义取决于网络分析的“规模”。 研究人员打算引入一种统计方法（所谓的自相似测度），该方法基于用连续更大的瓦片划分复杂网络，以揭示社交网络的模块结构，并研究这些模块对观察尺度的依赖性。通过这种方式，他们将研究模块的动态演化，然后是模块的模块等等，是否以类似的方式表现。同样，众所周知，大量的社会互动可能会在社会中创建具有不同属性的网络。根据初步结果，某些类型的社交网络在其特征上遵循这种自相似性，而另一些则没有。研究人员将根据自相似性对现有的社交网络进行分类，并研究模块如何在人群中出现。 这种模块化的重要性将在重要的应用中得到强调，例如对免疫工作效率的影响。 该项目涉及通过国际合作收集的许多不同的数据集，这些数据集在规模和准确性方面都代表了该领域的最新技术水平。 通过将数学工具应用于社交网络，研究人员旨在得出社会学家和物理学家共同感兴趣的结论。

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.