Greedily improving our own centrality in a network

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