  From transportation networks to complex infrastructures, and to social and
economic networks, a large variety of systems can be described in terms of
multiplex networks formed by a set of nodes interacting through different
network layers. Network robustness, as one of the most successful application
areas of complex networks, has also attracted great interest in both
theoretical and empirical researches. However, the vast majority of existing
researches mainly focus on the robustness of single-layer networks an
interdependent networks, how multiplex networks respond to potential attack is
still short of further exploration. Here we study the robustness of multiplex
networks under two attack strategies: layer node-based random attack and layer
node-based targeted attack. A theoretical analysis framework is proposed to
calculate the critical threshold and the size of giant component of multiplex
networks when a fraction of layer nodes are removed randomly or intentionally.
Via numerous simulations, it is unveiled that the theoretical method can
accurately predict the threshold and the size of giant component, irrespective
of attack strategies. Moreover, we also compare the robustness of multiplex
networks under multiplex node-based attack and layer node-based attack, and
find that layer node-based attack makes multiplex networks more vulnerable,
regardless of average degree and underlying topology. Our finding may shed new
light on the protection of multiplex networks.
