Many centrality measures have been proposed in the last
decade to assess the relative importance of vertices in a
complex network and to identify the role played by each
node in the network. Finding important nodes is useful to
estimate the potential damage that can be inflicted to the
structure of a network by removing particular nodes. In
this letter we show that it is always possible to set a
given eigenvector centrality for all the nodes in a weighted
network by tuning the weights of a very small subset of
nodes, called controlling set. We introduce a measure of
controllability for weighted networks based on the size of
the minimal controlling set, and propose two greedy
algorithms which are able to find sufficiently small
controlling sets. Experimental results reveal that even
large real networks have very small controlling sets, and
are therefore vulnerable to focused changes of edge weights
which can modify the eigenvector centrality of any node. |