Since the works of Watts and Strogatz (1998) on one hand, and Barabási and Albert (1999) on the other, graph theory has become a major mathematical field that provides a framework to handle network properties theoretically and enables us with very powerful tools to model and solve problems on networks. Understanding their graph structure is a key point in deriving efficient algorithms in large networks. In this school, we will cover theoretical aspects of graph structure analysis as well as applications on complex network studies with 9 lectures in two main axes: