Effect of Memory on the Dynamics of Random Walks on Networks

@article{Lambiotte2015EffectOM,
  title={Effect of Memory on the Dynamics of Random Walks on Networks},
  author={Renaud Lambiotte and Vsevolod Salnikov and Martin Rosvall},
  journal={ArXiv},
  year={2015},
  volume={abs/1401.0447}
}
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an analytical expression for the effect of memory on the spectral gap and thus, equivalently, on the characteristic time needed for the stochastic process to asymptotically reach equilibrium. Perturbation analysis shows that standard first-order Markov models can… 

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References

SHOWING 1-10 OF 108 REFERENCES
Generalized Master Equations for Non-Poisson Dynamics on Networks
TLDR
The effects of non-Poisson inter-event statistics on the dynamics of edges are examined, and the concept of a generalized master equation is applied to the study of continuous-time random walks on networks.
Temporal networks: slowing down diffusion by long lasting interactions
TLDR
The Laplacian spectrum of temporal networks is investigated and it is shown that the spectrum of the ensemble average of a temporal network has identical eigenmodes but smaller eigenvalues than the aggregate networks.
Burstiness and spreading on temporal networks
TLDR
It is shown that a detailed modeling of the temporal patterns observed in complex networks can change dramatically the properties of a spreading process, such as the ergodicity of a random walk process or the persistence of an epidemic.
Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks.
TLDR
This work introduces a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks and shows that compared with the time-aggregated network, non- Markovian characteristics can lead to both a slow-down or speed-up of diffusion.
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.
Thresholds for epidemic spreading in networks
TLDR
It is conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.
Effects of diffusion rates on epidemic spreads in metapopulation networks
It is often useful to represent the infectious dynamics of mobile agents by metapopulation models. In such a model, metapopulations form a static network, and individuals migrate from one
Natural human mobility patterns and spatial spread of infectious diseases
TLDR
A model for spatial epidemics explicitly taking into account bidirectional movements between base and destination locations on individual mobility networks is investigated and shows that a fully stochastic system exhibits a novel threshold for the attack ratio of an outbreak that is absent in diffusion and force of infection models.
Multiscale mobility networks and the spatial spreading of infectious diseases
TLDR
The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multiscale framework.
Synchronization in small-world systems.
TLDR
Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes.
...
...