A theory of tie-set graph and tie-set path - a graph theoretical study on robust network system

Aiming at the establishment of a graph theoretical basis for a network management system using loops in the network as basic management units, this paper presents tie-set graph theory and its useful properties, such as transformation of tie-set graph, meta-tie-set graph measure of tie-set graph and simplest tie-set graph. It is shown that proposed theory gives a theoretical basis and effective means for loop based network management. Distributed algorithms for finding the lightest tie-set path are presented that can apply to fault link avoidance and load balancing in an information network.