Zero Pearson coefficient for strongly correlated growing trees

2009/11/22 by S. N. Dorogovtsev, S. N. Dorogovt︠s︡ev, A. L. Ferreira +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #Data Visualization and Analytics #Linguistics #Mathematics #Pearson product-moment correlation coefficient #Philosophy #Statistics #Zero (linguistics) #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1103/physreve.81.031135

published as Phys. Rev. E 81, 031135 (2010) · 6 pages, 4 figures

arxiv created 2009/11/22 · openalex publication_date 2010/03/31 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We obtained Pearson's coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by m edges. We found that the Pearson coefficient is exactly zero in the infinite network limit for the recursive trees (m=1). If the number of connections of new vertices exceeds one (m>1), then the Pearson coefficient in the infinite networks equals zero only when the degree distribution exponent gamma does not exceed 4. We calculated the Pearson coefficient for finite networks and observed a slow power-law-like approach to an infinite network limit. Our findings indicate that Pearson's coefficient strongly depends on size and details of networks, which makes this characteristic virtually useless for quantitative comparison of different networks.

Citations

• Correlations in connected random graphs
• Organization of growing random networks
• Dynamical and Correlation Properties of the Internet
• Rate equation approach for correlations in growing network models
• Assortative Mixing in Networks
• Generation of arbitrarily two-point-correlated random networks
• The Structure and Function of Complex Networks