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Degree distributions under general node removal: Power-law or Poisson?

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Node removal in networked systems alters degree distributions. This study quantifies these changes, revealing two distinct regimes: one favoring power-law distributions and another favoring Poisson distributions, depending on removal strategy.

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Area of Science:

  • Network science
  • Complex systems analysis
  • Statistical physics

Background:

  • Network perturbations, like node removal, can cause structural loss, impacting network properties.
  • Previous research on node removal's effect on degree distributions shows conflicting results.
  • Understanding degree distribution changes is crucial for network analysis and dynamics.

Purpose of the Study:

  • To clarify the impact of node removal on the functional form of degree distributions in networked systems.
  • To quantify the distance between subnetwork degree distributions and reference distributions (Poisson and power-law).
  • To classify altered degree distributions under various node removal strategies, including hub protection.

Main Methods:

  • Utilized relative entropies to measure the divergence of subnetwork degree distributions from Poisson and power-law references.
  • Introduced general sequential node removal processes with varying levels of hub protection.
  • Employed direct node-removal simulations and solved rate equations for degree distributions.

Main Results:

  • Identified two distinct regimes in the parameter space based on relative entropy values.
  • One regime shows degree distributions closer to a power-law form.
  • The other regime shows degree distributions closer to a Poisson form.

Conclusions:

  • The functional form of degree distributions after node removal is dependent on the removal strategy.
  • The study provides a framework for classifying network alterations based on degree distribution changes.
  • Findings contribute to a deeper understanding of network robustness and dynamics under perturbations.