This comprehensive compendium discusses the basics of graph theory to its application, focusing on the application of graph theory to mobile communications. A mobile communication connects a mobile terminal and a base station wirelessly, and the base station enables communications all over the world via a wired and satellite communication system. This means that the mobile communication system includes wire and wireless technologies, and also hardware such as analog electric circuits, digital circuits and a software part such as computer algorithms. This useful reference text deeply studies how the network structure influences the performance of the corresponding system.