  We study the robustness properties of multiplex networks consisting of
multiple layers of distinct types of links, focusing on the role of
correlations between degrees of a node in different layers. We use generating
function formalism to address various notions of the network robustness
relevant to multiplex networks such as the resilience of ordinary- and mutual
connectivity under random or targeted node removals as well as the
biconnectivity. We found that correlated coupling can affect the structural
robustness of multiplex networks in diverse fashion. For example, for
maximally-correlated duplex networks, all pairs of nodes in the giant component
are connected via at least two independent paths and network structure is
highly resilient to random failure. In contrast, anti-correlated duplex
networks are on one hand robust against targeted attack on high-degree nodes,
but on the other hand they can be vulnerable to random failure.
