Are communities as strong as we think?

Many complex systems, from World Wide Web and online social networks to mobile networks, exhibit community structure in which nodes can be grouped into densely interconnected communities. This special structure has been exploited extensively to design better solutions for many operations and applications such as routing in wireless networks, worm containment and interest prediction in social networks. The outcome of these solutions are sensitive to the network structures, which raises an important question: can communities be broken easily in a network? To answer this question, we introduce a density-based problem formulation for analyzing the vulnerability of communities. Our approach includes the NP-completeness and a O(log k) approximation algorithm for solving the problem where k is the number of communities to be broken. Additionally, we analyze the vulnerability of communities in the context of arbitrary community detection algorithms. The empirical results show that communities are vulnerable to edge removal and in some cases the removal of a small fraction of edges can break the community structure.