For many real world systems ranging from biology to engineering, efficient network computation methods have attracted much attention in many applications. Generally, the performance of a network computation can be improved in two ways, i.e., rewiring and weighting. As a matter of fact, many real-world networks where an interpretation of efficient computation is relevant are weighted and directed. Thus, one can argue that nature might have assigned the optimal structure and weights to adjust the level of functionality. Indeed, in many neural and biochemical networks there is evidence that the synchronized and coordinated behavior may play important roles in the system’s functionality. The importance of the network weighting is not limited to the nature. In computer networks, for example, designing appropriate weights and directions for the connection links may enhance the ability of the network to synchronize the processes, thus leading the performance of computation to improve. In this paper, we propose a new two-mode weighting strategy by employing the network topological centralities including the degree, betweenness, closeness and communication neighbor graph. The weighting strategy consists of two modes, i.e., the original mode, in which the synchronizability is enhanced by increasing the weight of bridge edges, and the inverse version, in which the performance of community detection is improved by reducing the weight of bridge edges. We control the weight strategy by simply tuning a single parameter, which can be easily performed in the real world systems. We test the effectiveness of our model in a number of artificial benchmark networks as well as real-world networks. To the best of our knowledge, the proposed weighting strategy outperforms previously published weighting methods of improving the performance of network computation.