Graphs and their structure: the interplay between local and global properties of graphs

图作为简单和易于理解的模型，用于各种情况，如社会，协作，通信和运输网络以及化学结构和动态过程。图论的发展受到互联网的发展和由此产生的大型通信网络的深刻影响。特别令人感兴趣的是网络的全局结构与其局部属性之间的关系。更深入地理解网络的全局和局部属性之间的相互作用在算法过程中是有用的。一方面，我们建议建立新的全球和本地网络的属性/结构之间的连接，另一方面，我们建议使用某些网络类型的全球和本地结构之间的现有连接，以找到有效的解决方案，困难的网络问题。我们拟议的工作有四个主题，概述如下。

Graphs serve as simple and easily understood models for various situations such as social, collaboration, communication and transportation networks as well as for chemical structures and dynamical processes. The development of graph theory has been profoundly influenced by the evolution of the internet and resulting large communication networks. Of particular interest are relationships between the global structure of the network and its local properties. A deeper understanding of the interplay between global and local properties of a network is useful in algorithmic processes. On the one hand we propose to establish new connections between global and local properties/structures of networks and on the other hand we propose to use existing connections between global and local structures of certain network types to find efficient solutions for difficult network problems. Our proposed work has four main themes as outlined below.