  In the multidisciplinary field of Network Science, optimization of procedures
for efficiently breaking complex networks is attracting much attention from
practical points of view. In this contribution we present a module-based method
to efficiently break complex networks. The procedure first identifies the
communities in which the network can be represented, then it deletes the nodes
(edges) that connect different modules by its order in the betweenness
centrality ranking list. We illustrate the method by applying it to various
well known examples of social, infrastructure, and biological networks. We show
that the proposed method always outperforms vertex (edge) attacks which are
based on the ranking of node (edge) degree or centrality, with a huge gain in
efficiency for some examples. Remarkably, for the US power grid, the present
method breaks the original network of 4941 nodes to many fragments smaller than
197 nodes (4% of the original size) by removing mere 164 nodes (~3%) identified
by the procedure. By comparison, any degree or centrality based procedure,
deleting the same amount of nodes, removes only 22% of the original network,
i.e. more than 3800 nodes continue to be connected after that
