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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Measuring degree-degree association in networks.

Mathias Raschke¹, Markus Schläpfer, Roberto Nibali

¹Laboratory for Safety Analysis, ETH Zurich, CH-8092 Zurich, Switzerland.

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

|January 15, 2011

Summary

Pearson correlation coefficient is unreliable for heavy-tailed networks. Kendall-Gibbons

Area of Science:

Network Science
Statistical Analysis

Background:

The Pearson correlation coefficient is widely used to measure degree-degree association in complex networks.
Heavy-tailed degree distributions are common in real-world networks, posing challenges for standard analysis.
Existing methods may not accurately reflect network structure when dealing with skewed degree distributions.

Purpose of the Study:

To assess the applicability of association measures to heavy-tailed degree distributions in complex networks.
To evaluate the robustness of Pearson's correlation coefficient and Kendall-Gibbons' τ{b} under these conditions.

Main Methods:

Utilized a probabilistic representation of network structure.
Analyzed degree-degree association using theoretical arguments and numerical simulations.

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Compared the performance of Pearson's correlation coefficient against Kendall-Gibbons' τ{b}.

Main Results:

Pearson's correlation coefficient's dependency on network size was observed, even with similar association structures.
This size dependency hinders systematic comparisons across different real-world networks.
Kendall-Gibbons' τ{b} demonstrated significantly greater robustness in measuring degree-degree association.

Conclusions:

Pearson's coefficient is not a universally reliable measure for degree-degree association in networks with heavy-tailed distributions.
Kendall-Gibbons' τ{b} offers a more stable and dependable alternative for such network analyses.
The findings advocate for the use of more robust statistical measures in complex network research.