  Spectral centrality measures allow to identify influential individuals in
social groups, to rank Web pages by their popularity, and even to determine the
impact of scientific researches. The centrality score of a node within a
network crucially depends on the entire pattern of connections, so that the
usual approach is to compute the node centralities once the network structure
is assigned. We face here with the inverse problem, that is, we study how to
modify the centrality scores of the nodes by acting on the structure of a given
network. We prove that there exist particular subsets of nodes, called
controlling sets, which can assign any prescribed set of centrality values to
all the nodes of a graph, by cooperatively tuning the weights of their
out-going links. We show that many large networks from the real world have
surprisingly small controlling sets, containing even less than 5-10% of the
nodes. These results suggest that rankings obtained from spectral centrality
measures have to be considered with extreme care, since they can be easily
controlled and even manipulated by a small group of nodes acting in a
coordinated way.
