Numbering of Nodes in a Communication Network

The link deficit algorithm proposed by Steigletiz, Weiner and Kletman is a heuristic to generate a potential network topology. This heuristic begins by numbering the nodes at random. If the nodes are numbered in a systematic manner, the link deficit algorithm yields a starting network which needs relatively lesser amount of perturbation before an acceptable network is found. Few methods for systematic numbering of nodes in a computer communication network have been proposed in the literature. Earlier we have proposed two graph theory based method for systematic numbering of nodes in a computer communication network. The nodes are numbered based on the eccentricity values. However the nodes having the same eccentricity values will end up in a tie. This article aims at resolving the eccentricity tie.