  Many mobile networks are represented as graphs to obtain insight to their
connectivity and transmission properties. Among these properties centrality
resilience, that is, how well centralities, such as closeness and betweennesss,
are maintained under attacks is a critical factor for proper functioning of a
network. In this paper, we study the centrality resilience of complex networks
by developing attack models to disrupt the rank of the top path-based
centrality vertices. To develop our attack models, we extend the concept of
rich clubs of influential vertices to the more general framework of scattered
rich clubs. We define scattered rich clubs as dense subgraphs of high
centrality vertices that are spread (scattered) across the network. Finding
scattered rich clubs, although of polynomial time complexity, is extremely
expensive computationally. We use snowball sampling to identify these important
substructures as well as to identify which edges to target in our proposed
attack models. Our results over a set of real world networks demonstrate that
our proposed algorithm is effective in finding the single or scattered rich
clubs efficiently and in successfully disrupting the centrality rankings of the
network. To summarize, we propose sampling-based attack models for testing the
resilience of networks with respect to centrality rankings. As part of this
process, we introduce scattered rich clubs, a generalized form of the rich club
model, efficient algorithms to detect them, and demonstrate their relation to
network resilience.
