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

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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.