# Multilayer networks

@article{Kivel2013MultilayerN, 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={2013}, volume={2}, pages={203-271} }

The chapter “Multilayer Networks” introduces the topic of interconnected multilayer networks, analyzing them from a few fronts: types of multilayer networks, their mathematical description, the dynamics of random walks, and the centrality (versatility) of nodes. Multilayer networks appear naturally in real data as, in many cases, the relationships (links) between the elements (nodes) can be of different kinds. For example, people can be connected through friendship, family relations, or work…

## 2,485 Citations

### Novel Multiplex PageRank in Multilayer Networks

- Computer ScienceIEEE Access
- 2018

This paper exploits the concept of populations’ random migration in a multiplex transport network to propose a new Multiplex PageRank centrality measure, where the effects of influence and feedback between networks on the centrality of nodes are directly considered and is applied to an artificial duplex network.

### Graphlets in multilayer networks

- Computer ScienceJ. Complex Networks
- 2021

A general and principled graphlet framework forMultilayer networks which allows one to break any multilayer network into small multilayered building blocks and can be used to analyze the structural building blocks of myriad multilayers networks.

### Clustering Coefficients in Weighted Undirected Multilayer Networks

- Computer Science
- 2021

This work provides new local clustering coefficients for multilayer networks, looking at the network from different perspectives depending on the node’s position, as well as a global clustering coefficient for the whole network.

### Analysing Motifs in Multilayer Networks

- Computer ScienceArXiv
- 2019

It is found that multilayer motifs in social networks are more homogeneous across layers, indicating that different types of social relationships are reinforcing each other, while those in the transportation network are more complementary across layers.

### Multiplex PageRank in Multilayer Networks Considering Shunt

- Computer ScienceSciSec
- 2019

Findings indicate that considering the network with multilayers helps uncover the rankings of nodes, which are different from the rankings in a monotonous network.

### Ranking in interconnected multilayer networks reveals versatile nodes.

- Computer ScienceNature communications
- 2015

A mathematical framework is described that allows us to calculate centrality in multilayer networks and rank nodes accordingly, finding the ones that play the most central roles in the cohesion of the whole structure, bridging together different types of relations.

### Comparison of Inter-Layer Couplings of Multilayer Networks

- Computer Science2015 11th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS)
- 2015

Experimental results show that the properties of inter-layer couplings are crucial for the stability of detected communities, and this paper proposes generalization of Inter-layer Couplings of multilayer networks.

### A local perspective on community structure in multilayer networks

- Computer ScienceNetwork Science
- 2017

This work analyzes the local behavior of different random walks on multiplex networks and shows that they have very different bottlenecks, which correspond to rather different notions of what it means for a set of nodes to be a good community.

### Multilayer Social Networks

- Computer Science
- 2016

This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayers social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading.

### Clustering multilayer graphs with missing nodes

- Computer ScienceAISTATS
- 2021

This work proposes a new framework that allows for layers to be defined on different sets of nodes, and investigates several generalizations of well-known clustering methods in the complete setting to the incomplete one and proves some consistency results under the Multi-Layer Stochastic Block Model assumption.

## References

SHOWING 1-10 OF 425 REFERENCES

### 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.

### Multiplex PageRank

- Computer SciencePloS one
- 2013

Taking the multiplex nature of the network into account helps uncover the emergence of rankings of nodes that differ from the rankings obtained from one single layer, and provides support in favor of the salience of multiplex centrality measures, like Multiplex PageRank.

### 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.

### 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.

### 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.

### Statistical mechanics of multiplex networks: entropy and overlap.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

A statistical mechanics framework is introduced to describe multiplex ensembles in which the existence of a link in one layer is correlated with theexistence of a links in another layer, which implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers.

### 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.