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
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
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 multiplexExpand
...
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3
4
5
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