Graphs and complex networks

在过去的十年里，人们对真实世界中的复杂网络进行了大量的建模研究，例如网络的链接结构。图是由顶点和它们之间的边组成的自然模型，用于模拟和预测复杂网络的性质。我的目标是使用几何学、无限图和概率论的工具，为复杂网络设计和分析新的现实模型。Facebook和Twitter等在线社交网络(节点代表人，边对应社交互动)是一种重要的复杂网络类型。这种网络包含许多稠密的子图，代表紧密联系的社区。我将为在线社交网络提出新的进化模型，作为对其社区结构进行分类的一种方法。以网络为例，图表模型的应用可能会导致更高效的搜索引擎；在在线社交网络中，它们可能有助于绘制社会影响力的传播地图。

The last decade has witnessed a great deal of research on modelling real-world complex networks such as the link structure of the web. Graphs, consisting of vertices and edges between them, make natural models which simulate and predict properties of complex networks. My goals are to devise and analyze new realistic models for complex networks, using tools from geometry, infinite graphs, and probability theory. On-line social networks (where nodes represent people and edges correspond to social interactions) such as Facebook and Twitter, are an important type of complex network. Such networks contain many dense subgraphs representing tight-knit communities. I will propose new evolutionary models for on-line social networks, as an approach to classifying their community structure. Applications of graph models may lead, in the case of the web, to more efficient search engines; in on-line social networks, they may help map the spread of social influence.