Articulation points in multiplex networks

Many real systems can be efficiently represented by complex networks. Recently, the robustness of these networks under random or targeted attacks has been of interest. One of the strategies to dismantle a network involves identifying and removing articulation points. These are nodes that are critical to the network's connectivity; their removal causes the network to break into separate components. Most real-world networks are not isolated, but interacting, and can be viewed as multiplex networks. Inherent cascading failure within multiplex structures makes the definition of articulation points evading; an articulation point of a single monoplex layer loses this property due to removal by cascading failure within the parent multiplex network. We extend a consistent definition of articulation points and apply it to real and random multiplex networks. Moreover, we find that most of the real networks are vulnerable to the articulation points removal process. Through extensive simulations, we establish criteria for network resilience to this process across different types of random multiplex network models. These include two- and three-layer Erdős-Rényi multiplex networks, two-layer scale-free multiplex networks with varying degree exponents, and hyperbolic multiplex networks.