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Zero Pearson coefficient for strongly correlated growing trees.

Authors
  • Dorogovtsev, S N
  • Ferreira, A L
  • Goltsev, A V
  • Mendes, J F F
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
Mar 01, 2010
Volume
81
Issue
3 Pt 1
Pages
31135–31135
Identifiers
PMID: 20365725
Source
Medline
License
Unknown

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.

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