# Directed Percolation in Temporal Networks

@article{BadieModiri2022DirectedPI, title={Directed Percolation in Temporal Networks}, author={Arash Badie-Modiri and Abbas K. Rizi and M{\'a}rton Karsai and Mikko Kivel{\"a}}, journal={ArXiv}, year={2022}, volume={abs/2107.01510} }

Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study in complex systems for the last decade. However, while isotropic percolation theory successfully describes connectivity in static networks, a similar description has not been yet developed for temporal networks. Here address this problem and formalize a…

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## References

SHOWING 1-10 OF 79 REFERENCES

### Directed Percolation in Random Temporal Network Models with Heterogeneities

- Computer SciencePhysical review. E
- 2022

This work systematically analyzes random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods and finds that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities.

### Temporal percolation in activity-driven networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is shown in particular how the susceptible-infected-removed model on an activity-driven network can be mapped to the percolation problem up to a time given by the spreading rate of the epidemic process.

### Mapping temporal-network percolation to weighted, static event graphs

- Computer ScienceScientific Reports
- 2018

The dynamics of diffusion-like processes on temporal networks are influenced by correlations in the times of contacts. This influence is particularly strong for processes where the spreading agent…

### Efficient limited time reachability estimation in temporal networks

- Computer SciencePhysical review. E
- 2020

The proposed method gives simultaneous estimates of the in- or out-reachability of limited-waiting-time temporal paths from every possible starting point and time, which opens up the possibility to analyze reachability and dynamics of spreading processes on large temporal networks in completely new ways.

### Dynamic networks and directed percolation

- Computer Science
- 2010

The dynamic network undergoes a percolation phase transition at a critical concentration pc, that decreases with the rate r at which the network links are changed, and the behavior near criticality is universal and independent of r.

### Path lengths, correlations, and centrality in temporal networks

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

Differences between static and temporal properties are further highlighted in studies of the temporal closeness centrality, and correlations and heterogeneities in the underlying event sequences affect temporal path lengths, increasing temporal distances in communication networks and decreasing them in the air transport network.

### Approximating the Temporal Neighbourhood Function of Large Temporal Graphs

- Computer ScienceAlgorithms
- 2019

This paper first shows how the sketch approach can be applied to the case of temporal networks in order to approximately compute the sizes of the temporal cones of a temporal network, and subsequently shows how this approach can approximate the temporal neighborhood function of large temporal Networks in a few seconds.

### Restless reachability problems in temporal graphs.

- Computer Science, Mathematics
- 2020

This work presents an algebraic algorithmic framework based on constrained multilinear sieving for solving restless reachability problems in vertex-colored temporal graphs and proves that the algorithms presented are optimal under plausible complexity-theoretic assumptions.

### Weighted temporal event graphs

- Computer ScienceComputational Social Sciences
- 2019

This Chapter discusses a recently-introduced, more general framework that maps temporal-network structure into static graphs while retaining information on time-respecting paths and the time differences between their consequent events.