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Measurement error of network clustering coefficients under randomly missing nodes.

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Area of Science:

  • Network Science
  • Data Analysis
  • Graph Theory

Background:

  • Measurement error in network topology is a significant challenge in data analysis.
  • Understanding the discrepancy between original and collected network properties is crucial for accurate topology analysis.
  • The analytical measurement error of clustering coefficients, a fundamental network property, remains poorly understood.

Purpose of the Study:

  • To analytically and numerically investigate the measurement error of clustering coefficients in networks with randomly missing nodes.
  • To clarify the impact of missing data on global and average clustering coefficients.
  • To provide an analytical understanding of measurement errors in network properties.

Main Methods:

  • Derivation of the expected error for global and network average clustering coefficients in incomplete networks.
  • Analytical investigation of the relationship between missing nodes and clustering coefficient error.
  • Numerical simulations using Erdős-Rényi, Watts-Strogatz, and Barabási-Albert network models, plus real-world network datasets.

Main Results:

  • The global clustering coefficient of an incomplete network exhibits minimal expected error.
  • The network average clustering coefficient is systematically underestimated, with error dependent on graph-specific properties.
  • Simulation results on real-world networks with high clustering coefficients support analytical claims.

Conclusions:

  • The study provides analytical insights into measurement errors caused by missing network data.
  • Different clustering coefficients are affected differently by node loss.
  • Findings are validated on real-world networks, enhancing the understanding of network property analysis with incomplete data.