Measure of layer centrality in multilayer network

Many real-world complex systems consist of a set of basic units that are connected by different kinds of relationships. All types of such systems can be described by a multilayer network, where each link represents different types of interaction among the same set of nodes. In this paper, we present a general framework to characterize the influences (centrality) of layers. Furthermore, we propose two measures for layer centrality in terms of network connectivity under this framework. The basic idea of our measures consists in assigning more centrality value to layers that contribute more connectivity in a multilayer network. In other words, layers are more influential if more centrality values of links are assigned to them. We validate the measures on a real-world dataset of air transportation multilayer network and find that the measures are able to extract novel and useful information from the dataset.