Effect of Inter-layer Coupling on Multilayer Network Centrality Measures

The study of networks has been evolving because of its applications in diverse fields. Many complex systems involve multiple types of interactions and such systems are better modeled as multilayer networks. The question which are the most (or least) important nodes in a given network?, has gained substantial attention in the network science community. The importance of a node is known as centrality and there are multiple ways to define it. Extending the centrality measure to multilayer networks is challenging since the relative contribution of intra-layer edges vs. that of inter-layer edges to multilayer centrality is not straightforward. With the growing applications of multilayer networks, several attempts have been made to define centrality in multilayer networks in recent years. There are different ways of tuning the inter-layer couplings which may lead to different classes of centrality measures. In this article, we provide an overview of the recent works related to centrality in multilayer networks with a focus on key use cases and implications of the type of inter-layer coupling on centrality and subsequent uses of the different centrality measures. We discuss the effect of three popular inter-layer coupling methods viz. diagonal coupling between adjacent layers, diagonal coupling and cross coupling. We hope the colloquial tone of this article would make it a pleasant read for understanding the theoretical as well as experimental aspects of the work.