Nodes in a complex networked system often engage in more than one type of interactions among them; they form a multiplex network with multiple types of links. In real-world complex systems, a node's degree for one type of links and that for the other are not randomly distributed but correlated, which we term correlated multiplexity. In this paper, we study a simple model of multiplex random networks and demonstrate that the correlated multiplexity can drastically affect the properties of a giant component in the network. Specifically, when the degrees of a node for different interactions in a duplex Erdős-Rényi network are maximally correlated, the network contains the giant component for any nonzero link density. In contrast, when the degrees of a node are maximally anti-correlated, the emergence of the giant component is significantly delayed, yet the entire network becomes connected into a single component at a finite link density. We also discuss the mixing patterns and the cases with imperfect correlated multiplexity.

We study the effect of team and hierarchy on the waiting-time dynamics of priority-queue networks. To this end, we introduce generalized priority-queue network models incorporating interaction rules based on team-execution and hierarchy in decision making, respectively. It is numerically found that the waiting-time distribution exhibits a power law for long waiting times in both cases, yet with different exponents depending on the team size and the position of queue nodes in the hierarchy, respectively. The observed power-law behaviors have in many cases a corresponding single or pairwise-interacting queue dynamics, suggesting that the pairwise interaction may constitute a major dynamic consequence in the priority-queue networks. It is also found that the reciprocity of influence is a relevant factor for the priority-queue network dynamics.