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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Correlations in complex networks under attack.

Animesh Srivastava1, Bivas Mitra, Niloy Ganguly

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

Network attacks can alter network structure. Researchers developed analytical methods to predict topological changes and demonstrated that assortativity can be controlled by targeted node or edge removal.

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Area of Science:

  • Network Science
  • Complex Systems Analysis
  • Graph Theory

Background:

  • Network topology significantly influences system behavior and resilience.
  • Understanding how attacks affect network structure is crucial for robust system design.

Purpose of the Study:

  • To derive general expressions for network topological properties after node or edge removal.
  • To analyze the impact of various attack strategies on network assortativity and degree distribution.
  • To investigate the conditions under which network correlations can be induced or reversed.

Main Methods:

  • Development of analytical expressions for the degree-degree probability matrix and degree distribution.
  • Comparison of theoretical predictions with simulation results for assortativity coefficient evolution.
  • Analysis of different node and edge removal strategies and intensities.

Main Results:

  • General expressions for topological changes after attacks were obtained.
  • Analytical approach accurately predicts topological evolution under various attack scenarios.
  • Assortative networks can be transformed into disassortative ones, and vice versa, through controlled removal.
  • Targeted edge removal is necessary to induce correlations in initially uncorrelated networks.

Conclusions:

  • The study provides a robust analytical framework for understanding network response to attacks.
  • Network assortativity is controllable via fine-tuning node or edge removal strategies.
  • Findings have implications for designing resilient networks and understanding network dynamics.