Greedily Improving Our Own Centrality in A Network
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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