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Transmission efficiency and robustness are two important properties of various networks and a number of optimization strategies have been proposed recently. We propose a scheme to enhance the network performance by adding a small fraction of links (or edges) to the currently existing network topology, and we present four edge addition strategies for adding edges efficiently. We aim at minimizing the maximum node betweenness of any node in the network to improve its transmission efficiency, and a number of experiments on both Barabási–Albert (BA) and Erdös–Rényi (ER) networks have confirmed the effectiveness of our four edge addition strategies. Also, we evaluate the effect of some other measure metrics such as average path length, average betweenness, robustness, and degree distribution. Our work is very valuable and helpful for service providers to optimize their network performance by adding a …