There are several books on the applications of graph theory, but none of them are related to power systems applications. This book attempts to cover all applications of graph theory in the area of power systems. It consists of two parts. The first part, containing four Chapters, briefly introduces the basic concepts of graph theory, major properties, theorems, and algorithms in graph theory and network flow programming. This definitive treatment makes graph theory easy to understand. The second part, containing 10 Chapters, is the practical applications of graph theory and network flow programming to all kinds of power systems problems, which is the key part of the book. These applications include network flow calculation of power flow, classical economic power dispatch, security constrained economic dispatch, multi-areas system economic dispatch, reactive power optimization and pricing in multi-area environment, hydro-thermal power system operation, power system state estimation, secure economic automatic generation control, automatic contingency selection, distribution network optimization, and optimal load shedding. The treatment of each application includes the mathematical representation of power system problem, its relationship with graph theory and network flow programming, as well as the implementations accompanied by examples of power system application problem, solution, and results analysis. Each Chapter contains the related references that collectively form an extensive guide to the primary research literature.