  A practical approach to protecting networks against epidemic processes such
as spreading of infectious diseases, malware, and harmful viral information is
to remove some influential nodes beforehand to fragment the network into small
components. Because determining the optimal order to remove nodes is a
computationally hard problem, various approximate algorithms have been proposed
to efficiently fragment networks by sequential node removal. Morone and Makse
proposed an algorithm employing the non-backtracking matrix of given networks,
which outperforms various existing algorithms. In fact, many empirical networks
have community structure, compromising the assumption of local tree-like
structure on which the original algorithm is based. We develop an immunization
algorithm by synergistically combining the Morone-Makse algorithm and coarse
graining of the network in which we regard a community as a supernode. In this
way, we aim to identify nodes that connect different communities at a
reasonable computational cost. The proposed algorithm works more efficiently
than the Morone-Makse and other algorithms on networks with community
structure.
