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The mapping of temporal networks to directed percolation holds even for complex systems. Critical exponents remain robust despite network and dynamics variations, supporting scaling relationships in temporal reachability.

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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Temporal networks can be mapped to directed percolation problems.
  • This mapping relies on assumptions of local properties and randomness, which may not always hold.
  • Understanding the robustness of this mapping is crucial for analyzing complex temporal systems.

Purpose of the Study:

  • To challenge the assumptions of the directed percolation mapping for temporal networks.
  • To investigate the robustness of this mapping under various network topologies and dynamics.
  • To provide evidence for the validity of scaling relationships in temporal network reachability.

Main Methods:

  • Systematic analysis of random and regular network topologies.
  • Investigation of heterogeneous link-activation processes (bursty renewal, self-exciting).
  • Application of numerical simulation and finite-size scaling methods.

Main Results:

  • Critical percolation exponents are largely insensitive to structural and dynamical heterogeneities.
  • Recovered known scaling exponents from directed percolation on low-dimensional lattices.
  • Demonstrated robustness of the mapping for more complex temporal network models.

Conclusions:

  • The directed percolation mapping for temporal networks is robust to various heterogeneities.
  • Scaling relationships in limited-time reachability of temporal networks are supported by evidence.
  • This work advances the understanding of temporal network analysis through percolation theory.