Hidden features and information diffusion in large social networks

在社交网络中，基于用户之间的公共性程度来建立连接。通常，如果用户共享共同的功能或属于同一社区，则链接更有可能。网络形成可以通过假设节点嵌入特征空间中来建模，并且通过随机过程形成链接，该随机过程取决于底层空间中节点之间的距离。提出的研究的目的是开发模型和算法，将允许从大型网络的链接结构的潜在特征空间的提取。我将使用理论工具来研究节点的空间特征和链接结构之间的关系，使用无限极限来理解网络变大时的行为。我还将进一步开发和分析一个基于优先连接原则的增长网络的空间模型，该模型导致显示出常见特征的图形，例如幂律度分布，高聚类以及导致小世界属性的长链接的存在。

In social networks, connections are made based on a degree of communality between the users. Typically, links are more likely if users share common features or belong to the same community. Network formation can be modelled by assuming the nodes to be embedded in a feature space, and links to be formed through a stochastic process which depends on the distance between the nodes in the underlying space. The aim of the proposed research is to develop models and algorithms that will allow for the extraction of the latent feature space from the link structure of large networks. I will use theoretical tools to study the relationship between spatial features of the nodes and the link structure, using the infinite limit to understand the behaviour as the network gets large. I will also further develop and analyze a spatial model for growing networks, built on the principle of preferential attachment, which leads to graphs that exhibit commonly observed features such as a power law degree distribution, high clustering, and the presence of long links that lead to the small world property.