Multiplex measures for higher-order networks

A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order interactions among a collection of units. In this work, we introduce a comprehensive set of measures to describe structural connectivity patterns in multiplex hypergraphs, considering scales from node and hyperedge levels to the system's mesoscale. We validate our measures with three real-world datasets: scientific co-authorship in physics, movie collaborations, and high school interactions. This validation reveals new collaboration patterns, identifies trends within and across movie subfields, and provides insights into daily interaction dynamics. Our framework aims to offer a more nuanced characterization of real-world systems marked by both multiplex and higher-order interactions.