# A new framework for dynamical models on multiplex networks

@article{DeFord2018ANF, title={A new framework for dynamical models on multiplex networks}, author={Daryl R. DeFord and Scott D. Pauls}, journal={J. Complex Networks}, year={2018}, volume={6}, pages={353-381} }

Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics and statistics on these objects. We introduce a family of models of multiplex processes motivated by dynamical applications and investigate the properties of their spectra both theoretically and computationally. We study special cases of multiplex diffusion… Expand

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#### References

SHOWING 1-10 OF 58 REFERENCES

Mathematical Formulation of Multilayer Networks

- Physics, Mathematics
- 2013

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity,… Expand

The physics of spreading processes in multilayer networks

- Physics, Computer Science
- 2016

Progress is surveyed towards attaining a deeper understanding of spreading processes on multilayer networks, and some of the physical phenomena related to spreading processes that emerge from multilayered structure are highlighted. Expand

Spectral properties of the Laplacian of multiplex networks

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2013

This work derives an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them, and performs an asymptotic analysis that allow for analytical expressions for the full spectrum of eigenvalues. Expand

Diffusion dynamics on multiplex networks

- Physics, Computer Science
- Physical review letters
- 2013

P perturbative analysis is used to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers of the multiplex network, and allows us to understand the physics of diffusionlike processes on top of multiplex networks. Expand

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

- Computer Science, Physics
- Science
- 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. Expand

The structure and dynamics of multilayer networks

- Computer Science, Physics
- Physics Reports
- 2014

This work offers a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics. Expand

Structure of triadic relations in multiplex networks

- Physics, Computer Science
- 2015

This paper analyzes triadic relations and generalizes the idea of transitivity to multiplex networks, and illustrates that social networks have a strong tendency to promote redundancy by closing triads at every layer and that they thereby have a different type of multiplex transitivity from transportation networks, which do not exhibit such a tendency. Expand

Random walk centrality in interconnected multilayer networks

- Mathematics, Computer Science
- ArXiv
- 2015

The tensorial formalism recently proposed to characterize and investigate this kind of complex topologies is relied on, and two well known random walk centrality measures, the random walk betweenness and closeness centrality are extended to interconnected multilayer networks. Expand

Multilayer networks

- Computer Science, Physics
- J. Complex Networks
- 2014

The history of multilayer networks (and related concepts) is discussed and the exploding body of work on such networks is reviewed and attempts to generalize single-layer-network diagnostics to multilayers networks are reviewed. Expand

Discrete-time distributed consensus on multiplex networks

- Physics
- 2014

We introduce a discrete-time distributed consensus process on multi-layered complex networks represented by multiplex graphs. The proposed consensus process can be characterized with a multiplex… Expand