Fragmenting networks by targeting collective influencers at a mesoscopic level

TL;DR

This paper introduces a network fragmentation method targeting community-connecting nodes by combining the Morone-Makse algorithm with community coarse graining, improving efficiency on community-structured networks.

Contribution

It develops a novel immunization algorithm that synergistically combines existing algorithms with community coarse graining to better target influential nodes.

Findings

The new algorithm outperforms existing methods on community-structured networks.

It efficiently identifies nodes connecting different communities.

The approach improves network fragmentation effectiveness.

Abstract

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.