Title: Centralities of Nodes and Influences of Layers in Large Multiplex Networks,
Abstract: We formulate and propose an algorithm (MultiRank) for the ranking of nodes
and layers in large multiplex networks. MultiRank takes into account the full
multiplex network structure of the data and exploits the dual nature of the
network in terms of nodes and layers. The proposed centrality of the layers
(influences) and the centrality of the nodes are determined by a coupled set of
equations. The basic idea consists in assigning more centrality to nodes that
receive links from highly influential layers and from already central nodes.
The layers are more influential if highly central nodes are active in them. The
algorithm applies to directed/undirected as well as to weighted/unweighted
multiplex networks. We discuss the application of MultiRank to three major
examples of multiplex network datasets: the European Air Transportation
Multiplex Network, the Pierre Auger Multiplex Collaboration Network and the FAO
Multiplex Trade Network.