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Multilayer networks

  1. Mikko Kivelä
  1. Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
  1. Alex Arenas
  1. Departament d'Enginyeria Informática i Matemátiques, Universitat Rovira I Virgili, 43007 Tarragona, Spain
  1. Marc Barthelemy
  1. Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191, Gif-sur-Yvette, France and Centre d'Analyse et de Mathématiques Sociales, EHESS, 190-198 avenue de France, 75244 Paris, France
  1. James P. Gleeson
  1. MACSI, Department of Mathematics & Statistics, University of Limerick, Limerick, Ireland
  1. Yamir Moreno
  1. Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50018, Spain and Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain
  1. Mason A. Porter

+ Author Affiliations

  1. Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, UK
  1. Corresponding author. Email: porterm@maths.ox.ac.uk
  1. Edited by: Ernesto Estrada

  • Received October 16, 2013.
  • Accepted April 23, 2014.

Abstract

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such ‘multilayer’ features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize ‘traditional’ network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other and provide a thorough discussion that compares, contrasts and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.

Key words

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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  1. jcomplexnetw 2 (3): 203-271. doi: 10.1093/comnet/cnu016
  1. This article is Open AccessOA
  2. All Versions of this Article:
    1. cnu016v1
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