Greedily Improving Our Own Closeness Centrality in a Network

The closeness centrality is a well-known measure of importance of a vertex within a given complex network. Having high closeness centrality can have positive impact on the vertex itself: hence, in this paper we consider the optimization problem of determining how much a vertex can increase its centrality by creating a limited amount of new edges incident to it. We will consider both the undirected and the directed graph cases. In both cases, we first prove that the optimization problem does not admit a polynomial-time approximation scheme (unless P = NP), and then propose a greedy approximation algorithm (with an almost tight approximation ratio), whose performance is then tested on synthetic graphs and real-world networks.