  Recent advances have focused mainly on the resilience of the monoplex network
in attacks targeting random nodes or links, as well as the robustness of the
network against cascading attacks. However, very little research has been done
to investigate the robustness of nodes in multiplex networks against targeted
attacks. In this paper, we first propose a new measure, MultiCoreRank, to
calculate the global influence of nodes in a multiplex network. The measure
models the influence propagation on the core lattice of a multiplex network
after the core decomposition. Then, to study how the structural features can
affect the influence robustness of nodes, we compare the dynamics of node
influence on three types of multiplex networks: assortative, neutral, and
disassortative, where the assortativity is measured by the correlation
coefficient of the degrees of nodes across different layers. We found that
assortative networks have higher resilience against attack than neutral and
disassortative networks. The structure of disassortative networks tends to
break down quicker under attack.
