Analyzing networks as one of the most basic systems in the communications, telecommunication and internet networks has always been a concern for many researchers and craftsmen, so today we are witnessing a new evolution in the field of network security and reliability. A network is a collection of nodes and links that some particular nodes are called terminals. Rail station, road intersections are some example for nodes and railways, connection between the components of a network are some examples for links. A network is defined by the triplet N = (V,E, T), that V and E represents the node and the link set respectively and T is a subset of V that called terminal set, we suppose |V|= m and |E|= n. In fact each network can be modeled using a graph of nodes and edges. For example, a tree network is a collection of sub-networks which every two nodes are connected with a single edge. Failure of the components of a network (links or nodes) occurs on the basic of a stochastic mechanism and the failure of a link means the erase of the link and the failure of a node means that all links incident to that node are erased.
