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Generalized theory for node disruption in finite-size complex networks.

Bivas Mitra¹, Niloy Ganguly, Sujoy Ghose

¹Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur 721302, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

This summary is machine-generated.

Complex networks change after node removal. A new formula predicts degree distribution changes and network stability under attacks, with finite network corrections to percolation thresholds.

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Area of Science:

Network science
Complex systems analysis
Statistical physics

Background:

Complex networks are vulnerable to node removal during failures or attacks.
Understanding network structural changes is crucial for stability analysis.

Purpose of the Study:

To develop a general method for computing the degree distribution of networks after node removal.
To establish a general condition for the stability of complex networks against arbitrary attacks.
To derive an expression for the percolation threshold under specific attack strategies.

Main Methods:

Derivation of a simple formula for the degree distribution of a distorted network.
Development of a general condition for network stability based on the derived formula.
Application of the formalism to calculate the percolation threshold under power-law degree-based attacks.

Main Results:

A straightforward formula accurately computes the degree distribution of complex networks after node disturbances.
A general condition for the stability of noncorrelated finite complex networks under arbitrary attacks was established.
An expression for the percolation threshold (f_c) was derived for power-law attacks (f_k ~ k^gamma).
Finite-size correction (scaling as N^-1) to the percolation threshold for finite networks was identified.

Conclusions:

The developed formalism provides an efficient way to analyze network stability and predict structural changes.
The findings offer insights into the resilience of finite complex networks compared to infinite network models.
The study contributes to a deeper understanding of network robustness under targeted or random attacks.