The electrical resistance of a graph captures its commute and cover times
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Network robustness and graph topology
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Theory, Volume 1, Queueing Systems
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Communication nets; stochastic message flow and delay
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Making routing robust to changing traffic demands: algorithms and evaluation
IEEE/ACM Transactions on Networking (TON)
Minimizing Effective Resistance of a Graph
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Survival value of communication networks
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Betweenness centrality and resistance distance in communication networks
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Robustness to the environmental variations is an important feature of any reliable communication network. This paper reports on a network theory approach to the design of such networks where the environmental changes are traffic fluctuations, topology modifications, and changes in the source of external traffic. Motivated by the definition of betweenness centrality in network science, we introduce 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 use the average normalized traffic-aware betweenness, which is referred to as traffic-aware network criticality (TANC), as our main metric to quantify the robustness of a network. We show that TANC is directly related to some important network performance metrics, such as average network utilization and average network cost. We prove that TANC is a linear function of end-to-end effective resistances of the graph. As a result, TANC is a convex function of link weights and can be minimized using convex optimization techniques. We use semi-definite programming method to study the properties of the optimization problem and derive useful results to be employed for robust network planning purposes.