Some Methods of Finding Minimum Paths and the Importance of Reliability for a Complex System

This article will include three important methods for extracting minimal path sets from a complex network, and a comparison will be made between these methods to choose the best one for accessing minimal path sets. Also, this article will discuss HEWEIDY'S METHOD, which is a new and effective method for calculating the importance of each component of a complex network and its levels. This method depends entirely on the relationship between minimal path sets and minimal cut sets, and the latter we will extract from minimal path sets.