Betweenness centrality and resistance distance in communication networks

In this article we report on applications and extensions of weighted graph theory in the design and control of communication networks. We model the communication network as a weighted graph and use the existing literature in graph theory to study its behavior. We are particularly interested in the notions of betweenness centrality and resistance distance in the context of communication networks. We argue that in their most general form, the problems in a communication network can be converted to either the optimal selection of weights or optimal selection of paths based on the present values of weights in a graph. Motivated by this, we propose a two-loop general architecture for the control of networks and provide directions to design appropriate control algorithms in each control loop. We show that the total resistance distance (network criticality) of a graph has very useful interpretations in the context of communication networks; therefore, we propose to use network criticality as the main objective function, and we provide guidelines to design the control loops to minimize network criticality. We also discuss the development of new directed weighted graph models and their application to communication networks.