Analyzing networks requires complex algorithms to extract meaningful information. Centrality metrics have shown to be correlated with the importance and loads of the nodes in network traffic. Here, we are interested in the problem of centrality-based network management. The problem has many applications such as verifying the robustness of the networks and controlling or improving the entity dissemination. It can be defined as finding a small set of topological network modifications which yield a desired closeness centrality configuration. As a fundamental building block to tackle that problem, we propose incremental algorithms which efficiently update the closeness centrality values upon changes in network topology, i.e., edge insertions and deletions. Our algorithms are proven to be efficient on many real-life networks, especially on small-world networks, which have a small diameter and a spike-shaped shortest distance distribution. In addition to closeness centrality, they can also be a great arsenal for the shortest-path-based management and analysis of the networks. We experimentally validate the efficiency of our algorithms on large networks and show that they update the closeness centrality values of the temporal DBLP-coauthorship network of 1.2 million users 460 times faster than it would take to compute them from scratch. To the best of our knowledge, this is the first work which can yield practical large-scale network management based on closeness centrality values.