Survivability of communication networks

Connectivity, edge connectivity and connectivity pair are the concepts often used to indicate the survivability of communication networks. These parameters indicate the minimum number of communication stations or communication lines that need to be destroyed to put the system out of use. Since the number of work to destroy a communication station or a communication line is not always the same, the weight of a vertex or an edge is the number of work needed to destroy the corresponding station or line. Three new concepts - weighted connectivity, weighted edge connectivity and weighted mixed connectivity - were proposed. These parameters are generalizations of connectivity, edge connectivity and connectivity pair, and they are more precise in indicating the survivability of communication networks. Efficient algorithms for computing these parameters were proposed on the basis of Ford-Fulkerson's labeling method.