Abstract
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.
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