On Traffic-Aware Betweenness and Network Criticality

This paper introduces a new network science metric to evaluate the relative load on different links and nodes of a communication network. Motivated by the definition of random-walk betweenness in graph theory, we define the notion of traffic-aware betweenness (TAB) for data networks, where usually an explicit (or implicit) traffic matrix governs the distribution of external traffic into the network. We study the relationship between TAB and average network utilization and show that the average normalized traffic-aware betweenness, which is referred to as traffic-aware network criticality (TANC) is a linear function of end-to-end effective resistances (or network criticalities) of the graph. As a result, TANC is a convex function of link weights and can be minimized using convex optimization techniques. We construct a semidefinite program to solve this convex optimization problem and evaluate its optimal solution on some well-known graph topologies.