Analytical approach to network inference: Investigating degree distribution
Gloria Cecchini1, Björn Schelter2
1Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Meston Building, Meston Walk, Aberdeen, AB24 3UE, United Kingdom and Institute of Physics and Astronomy, University of Potsdam, Campus Golm, Karl-Liebknecht-Straße 24/25, D-14476, Potsdam-Golm, Germany.
Physical Review. E
|September 27, 2018
Summary
Network reconstruction can introduce false positive and false negative errors. This study analytically analyzes their impact on vertex degree distribution and provides a method to correct it for accurate network analysis.
Area of Science:
- Network Science
- Graph Theory
- Data Analysis
Background:
- Network reconstruction is prone to errors, specifically false positives and false negatives regarding link presence.
- These errors can significantly distort the observed vertex degree distribution, a key network property.
- Understanding and correcting for these errors is crucial for accurate network analysis.
Purpose of the Study:
- To analytically investigate the influence of false positive and false negative errors on vertex degree distribution.
- To derive an analytical formula for the density of the biased vertex degree distribution.
- To develop a reliable procedure for reconstructing the true vertex degree distribution from inferred networks.
Main Methods:
- Analytical derivation of the vertex degree distribution under error conditions.
- Formulation of a mathematical model to quantify the bias introduced by errors.
- Development of an inverse method to correct the biased distribution using error estimates.
Main Results:
- The study provides an analytical formula for the density of the vertex degree distribution affected by false positive and false negative errors.
- A reliable analytical procedure is established to reconstruct the true vertex degree distribution.
- The method leverages estimates of false positive and false negative errors, potentially from simulation studies.
Conclusions:
- False positive and false negative errors systematically bias the vertex degree distribution in reconstructed networks.
- The developed analytical framework and reconstruction procedure enable accurate estimation of the true vertex degree distribution.
- This work offers a valuable tool for network scientists dealing with imperfect network data.
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