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

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.