# Centralities of Nodes and Influences of Layers in Large Multiplex Networks

## TL;DR

This paper introduces MultiRank, an algorithm for ranking nodes and layers in large multiplex networks, considering their full structure and dual nature, applicable to various types of networks.

## Contribution

The paper presents a novel algorithm, MultiRank, that simultaneously ranks nodes and layers in multiplex networks by leveraging their interconnected structure.

## Key findings

- MultiRank effectively ranks nodes and layers in diverse multiplex networks.
- The algorithm accounts for directed, undirected, weighted, and unweighted networks.
- Application examples demonstrate its versatility and practical relevance.

## 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.