Betweenness is a well-known centrality measure that ranks the nodes according to their participation in the shortest paths of a network. In several scenarios, having a high betweenness can have a positive impact on the node itself. Hence, in this article, 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. In particular, we study the problem of maximizing the betweenness score of a given node—Maximum Betweenness Improvement (MBI)—and that of maximizing the ranking of a given node—Maximum Ranking Improvement (MRI). We show that MBI cannot be approximated in polynomial-time within a factor (1−1/2e) and that MRI does not admit any polynomial-time constant factor approximation algorithm, both unless P = NP . We then propose a simple greedy approximation algorithm for MBI with an almost tight approximation ratio and we test its performance on several real-world networks. We experimentally show that our algorithm highly increases both the betweenness score and the ranking of a given node and that it outperforms several competitive baselines. To speed up the computation of our greedy algorithm, we also propose a new dynamic algorithm for updating the betweenness of one node after an edge insertion, which might be of independent interest. Using the dynamic algorithm, we are now able to compute an approximation of MBI on networks with up to 10 ⁵ edges in most cases in a matter of seconds or a few minutes.

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.

Social link recommendation systems, like "People-you-may-know" on Facebook, "Who-to-follow" on Twitter, and "Suggested-Accounts" on Instagram assist the users of a social network in establishing new connections with other users. While these systems are becoming more and more important in the growth of social media, they tend to increase the popularity of users that are already popular. Indeed, since link recommenders aim at predicting users' behavior, they accelerate the creation of links that are likely to be created in the future, and, as a consequence, they reinforce social biases by suggesting few (popular) users, while giving few chances to the majority of users to build new connections and increase their popularity.In this paper we measure the popularity of a user by means of its social influence, which is its capability to influence other users' opinions, and we propose a link recommendation algorithm that evaluates the links to suggest according to their increment in social influence instead of their likelihood of being created. In detail, we give a constant factor approximation algorithm for the problem of maximizing the social influence of a given set of target users by suggesting a fixed number of new connections. We experimentally show that, with few new links and small computational time, our algorithm is able to increase by far the social influence of the target users. We compare our algorithm with several baselines and show that it is the most effective one in terms of increased influence.

The betweenness is a well-known measure of centrality of a node in a network. We consider the problem of determining how much a node can increase its betweenness centrality by creating a limited amount of new edges incident to it. If the graph is directed, this problem does not admit a polynomial-time approximation scheme (unless P=NP) and a simple greedy approximation algorithm guarantees an almost tight approximation ratio [E. D. Demaine and M. Zadimoghaddam. Minimizing the diameter of a network using shortcut edges. In Proc. of the 12th Scandinavian Symp. and Work. on Algorithm Theory (SWAT), volume 6139 of LNCS, pages 420–431. Springer, 2010].In this paper we focus on the undirected graph case: we show that also in this case the problem does not admit a polynomial-time approximation scheme (unless P=NP). Moreover, we show that, differently from the directed case, the greedy algorithm can have an unbounded approximation ratio. In order to test the practical performance of the greedy algorithm, we experimentally measured its efficiency in term of ranking improvement, comparing it with another algorithm that simply adds edges to the nodes that have highest betweenness. Our experiments show that the greedy algorithm adds only few edges in order to increase the betweenness of a node and to reach the top positions in the ranking. Moreover, the greedy algorithm outperforms the second approach