Classes of random walks on temporal networks with competing timescales

@article{Petit2019ClassesOR,
  title={Classes of random walks on temporal networks with competing timescales},
  author={Julien Petit and Renaud Lambiotte and Timot{\'e}o Carletti},
  journal={Applied Network Science},
  year={2019},
  volume={4},
  pages={1-20}
}
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the co-existence of different timescales in the system. Here, we introduce random walks on general stochastic temporal networks allowing for lasting interactions, with up to three competing timescales. We then compare the mean resting time and stationary state of different… 

Random Walks on Dense Graphs and Graphons

This work focuses on two classes of processes on dense weighted graph, in discrete and in continuous time, whose dynamics are encoded in the transition matrix and the random-walk Laplacian, and applies the spectral theory of operators to characterize the relaxation time of the process in the continuum limit.

Random walks on hypergraphs

This work contributes to unraveling the effect of higher-order interactions on diffusive processes in higher- order networks, shedding light on mechanisms at the heart of biased information spreading in complex networked systems.

Diffusion profile embedding as a basis for graph vertex similarity

A tool developed to characterize the accuracy of the similarity values in detecting community structures, the uncertainty index, is introduced in this paper as a measure of the quality of similarity methods.

Research on Behavior of Two New Random Entity Mobility Models in 3-D Space

It was seen that the proposed two models achieved better results than the existing models in 3D after 2D in 2D space, and it has been measured that the RP model can deliver the message to the base with less delay than other models.

Exposure theory for learning complex networks with random walks

Exposure theory is introduced, a statistical mechanics framework that predicts the learning of nodes and edges across several types of networks, including weighted and temporal, and shows that edge learning follows a universal trajectory.

Novel random models of entity mobility models and performance analysis ofrandom entity mobility models

  • Metin Bilgin
  • Computer Science
    Turkish J. Electr. Eng. Comput. Sci.
  • 2020
Two new models (random point and random journey) were proposed as alternatives to existing REMMs and their performances were compared to those that are currently used prevalently (random waypoint, random walk, and random direction).

References

SHOWING 1-10 OF 58 REFERENCES

Random walk on temporal networks with lasting edges

This work proposes a comprehensive analytical and numerical treatment on directed acyclic graphs of random walks on dynamical networks where edges appear and disappear during finite time intervals and introduces a general analytical framework to characterize such non-Markovian walks.

Random walks and search in time-varying networks.

This work considers a model for time-varying networks created from the activity potential of the nodes and derives solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks.

Pattern Formation on Networks with Reactions: A Continuous Time Random Walk Approach

We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW). The non-trivial incorporation of the…

Characterizing continuous time random walks on time varying graphs

Conditions under which the CTRW is a stationary and ergodic time varying dynamic graph are established and the stationary distribution of the walker is characterized.

Fundamental structures of dynamic social networks

It is shown that at the right temporal resolution, social groups can be identified directly in the dynamic social network of a densely-connected population of ∼1,000 individuals, as well as their telecommunication networks, online social media contacts, geolocation, and demographic data.

Hopping in the Crowd to Unveil Network Topology.

It is shown that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects.

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks.

It is shown that compared with the time-aggregated network, non-Markovian characteristics can lead to both a slow-down or speed-up of diffusion, which can even outweigh the decelerating effect of community structures in the static topology.

Elephants can always remember: exact long-range memory effects in a non-Markovian random walk.

We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss…
...