Multilayer Networks

M. Kivelä et al [2014]., Journal of Complex Networks, Vol. 2, No. 3: 203–271

69 Pages Posted: 18 Oct 2013 Last revised: 20 Apr 2015

See all articles by Mikko Kivela

Mikko Kivela

Aalto University

Alex Arenas

Rovira i Virgili University - Departament d'Enginyeria Informatica i Matematiques

Marc Barthelemy

Centre d’Analyse et de Mathématique Sociales (CAMS, CNRS-EHESS)

James P. Gleeson

University of Limerick, Ireland

Yamir Moreno

University of Zaragoza

Mason Alexander Porter

University of Oxford

Date Written: August 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.

Keywords: networks, multilayer networks, multiplex networks, interdependent networks, networks of networks, interconnected networks

Suggested Citation

Kivela, Mikko and Arenas, Alex and Barthelemy, Marc and Gleeson, James P. and Moreno, Yamir and Porter, Mason Alexander, Multilayer Networks (August 2014). M. Kivelä et al [2014]., Journal of Complex Networks, Vol. 2, No. 3: 203–271 , Available at SSRN: https://ssrn.com/abstract=2341334 or http://dx.doi.org/10.2139/ssrn.2341334

Mikko Kivela

Aalto University ( email )

P.O. Box 21210
Helsinki, 00101
Finland

Alex Arenas

Rovira i Virgili University - Departament d'Enginyeria Informatica i Matematiques ( email )

Campus Sescelades
Avinguda dels Països Catalans, 26
43006 Tarragona
Spain

Marc Barthelemy

Centre d’Analyse et de Mathématique Sociales (CAMS, CNRS-EHESS) ( email )

James P. Gleeson

University of Limerick, Ireland ( email )

MACSI
Dept of Mathematics and Statistics
Limerick
Ireland

HOME PAGE: http://www.ul.ie/gleesonj

Yamir Moreno

University of Zaragoza ( email )

Gran Via 2
Zaragoza, 50005
Spain

Mason Alexander Porter (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

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