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Network Modification using a Novel Gramian-based Edge Centrality

Modifying the structure of man-made and natural networked systems has become increasingly feasible due to recent technological advances. This flexibility offers great opportunities to save resources and improve controllability and energy efficiency. In contrast (and dual) to the well-studied optimal actuator placement problem, this work focuses on improving network controllability by adding and/or re-weighting network edges while keeping the actuation structure fixed. First a novel energy-based edge centrality measure is proposed and then its relationship with the gradient (with respect to edge weights) of the trace of the controllability Gramian is rigorously characterized. Finally, a network modification algorithm based on the proposed measure is proposed and its efficacy in terms of computational complexity and controllability enhancement is numerically demonstrated.