Abstract: In this study, some concepts of graph theory have been introduced to evaluate the reliability of complex systems inside aircraft. For the purpose of establishing the structure function to find the reliability of complex system (bridge network) as well as we will use some concepts in the probability theory and apply it on the graph theory such as conditional probability approach that depend on it Bayes theorem method which will be use it in this study to evaluate the reliability of electrical aircraft system, all figures and equations are written by wolfram mathematica programming.