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Linear relation on the correlation in complex networks.

C W Ma1, K Y Szeto

  • 1Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 23, 2006
PubMed
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Complex networks exhibit a linear correlation between node degree and neighbor degrees, extending the Aboav-Weaire law. This finding offers a new perspective on network correlation, complementing existing methods.

Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Complex networks display intricate correlation patterns.
  • Existing methods like Pearson correlation and power laws describe these patterns.
  • The Aboav-Weaire law characterizes correlations in cellular structures.

Purpose of the Study:

  • To investigate a general linear relation for node degree and neighbor degrees in complex networks.
  • To extend the Aboav-Weaire law to diverse real-world network classes.
  • To provide an analytical framework for this linear relation in standard network models.

Main Methods:

  • Analysis of six classes of real-world networks.
  • Derivation of an analytical expression for the linear relation.
  • Examination of Erdos-Renyi, Watts-Strogatz, and Barabasi-Albert network models.

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Main Results:

  • A universal linear relation was identified between node degree and the total degrees of its neighbors.
  • This relation is analytically described by a single parameter and moments of the degree distribution.
  • The intercept's sign correlates with the network's assortativity.

Conclusions:

  • The linear relation offers a novel and complementary perspective on complex network correlations.
  • This approach simplifies the understanding of degree-neighbor degree relationships.
  • The findings provide a new tool for network analysis and characterization.