# Multilayer networks

@article{Kivel2014MultilayerN, title={Multilayer networks}, author={Mikko Kivel{\"a} and Alex Arenas and Marc Barthelemy and James P. Gleeson and Yamir Moreno and Mason A. Porter}, journal={J. Complex Networks}, year={2014}, volume={2}, pages={203-271} }

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…

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## References

SHOWING 1-10 OF 493 REFERENCES

Mathematical Formulation of Multilayer Networks

- Computer Science
- 2013

This paper introduces a tensorial framework to study multilayer networks, and discusses the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvectorcentrality, modularity, von Neumann entropy, and diffusion—for this framework.

Layer aggregation and reducibility of multilayer interconnected networks

- Computer ScienceArXiv
- 2014

This work introduces a method, based on information theory, to reduce the number of layers in multilayer networks, while minimizing information loss, and proves its applicability to an extended data set of protein-genetic interactions.

Centrality in Interconnected Multilayer Networks

- Computer ScienceArXiv
- 2013

It is shown, both theoretically and numerically, that using the weighted monoplex obtained by aggregating the multilayer network leads, in general, to relevant differences in ranking the nodes by their importance.

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

- Computer ScienceScience
- 2010

A generalized framework of network quality functions was developed that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices.

Multiplexity-facilitated cascades in networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This work generalizes the threshold cascade model to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active, and shows that both combining layers and splitting a network into layers facilitate cascades.

Complex Networks: Structure and Dynamics

- Computer Science
- 2014

The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

Emergence of network features from multiplexity

- Computer ScienceScientific reports
- 2013

This work analyzes the structural properties of an intrinsically multilayered real network, the European Air Transportation Multiplex Network in which each commercial airline defines a network layer, and discusses how the topology of each layer affects the emergence of structural properties in the aggregate network.

The architecture of complex weighted networks.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2004

This work studies the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively, and defines appropriate metrics combining weighted and topological observables that enable it to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices.

Investigating the topology of interacting networks

- Environmental Science
- 2011

A novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks is introduced and the new measure “cross-betweenness” identifies regions which are particularly important for mediating vertical wind field interactions.