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In this paper, we consider a network of agents with Laplacian dynamics, andstudy the problem of improving network robustness by adding a maximum number ofedges within the network while preserving a lower bound on its strongstructural controllability (SSC) at the same time. Edge augmentation increasesnetwork's robustness to noise and structural changes, however, it could alsodeteriorate network controllability. Thus, by exploiting relationship betweennetwork controllability and distances between nodes in graphs, we formulate anedge augmentation problem with a constraint to preserve distances betweencertain node pairs, which in turn guarantees that a lower bound on SSC ismaintained even after adding edges. In this direction, first we choose a nodepair and maximally add edges while maintaining the distance between selectednodes. We show that an optimal solution belongs to a certain class of graphscalled clique chains. Then, we present an algorithm to add edges whilepreserving distances between a certain collection of nodes. Further, we presenta randomized algorithm that guarantees a desired approximation ratio with highprobability to solve the edge augmentation problem. Finally, we evaluate ourresults on various networks.

Improving Network Robustness through Edge Augmentation While Preserving Strong Structural Controllability