TO DO!
% Given a connected graph $G=(V,E)$, the closeness centrality of a vertex $v$ is defined as $ \frac{n-1}{\sum_{w \in V} d(v,w)}$. This measure is widely used in the analysis of real-world complex networks, and the problem of selecting the $k$ most central vertices has been deeply analysed in the last decade. However, this problem is computationally not easy, especially for large networks. I propose an algorithm for selecting the $k$ most central nodes in a graph: I experimentally show that this algorithm improves significantly both the textbook algorithm, which is based on computing the distance between all pairs of vertices, and the state of the art. Finally, as a case study, I compute the $10$ most central actors in the IMDB collaboration network, where two actors are linked if they played together in a movie.

% Da cambiare le parole, preso dal paper