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The "center" of a data set is also a way of describing location. The two most widely used measures of the "center" of the data are the mean (average) and the median. The words "mean" and "average" are often used interchangeably. The substitution of one word for the other is common practice. The technical term is "arithmetic mean" and "average" is technically a center location. However, in practice among non-statisticians,...
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Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
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Betweenness centrality in a weighted network.

Huijuan Wang1, Javier Martin Hernandez, Piet Van Mieghem

  • 1Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

Network traffic analysis reveals that link betweenness in overlay networks follows a power law distribution, particularly in the strong disorder limit where transport concentrates on the minimum spanning tree (MST). This exponent correlates with degree variance.

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Area of Science:

  • Network Science
  • Complex Systems Analysis
  • Statistical Physics

Background:

  • Overlay networks, such as peer-to-peer and virtual private networks, are often analyzed as subgraphs of the union of all shortest path trees.
  • Understanding traffic flow and link importance (betweenness) within these networks is crucial for network design and management.
  • Network disorder, controlled by link weight distributions, significantly impacts transport dynamics.

Purpose of the Study:

  • To investigate the betweenness distribution of links within overlay networks, specifically focusing on the impact of network disorder.
  • To analyze how different tree structures and degree distributions influence traffic flow patterns.
  • To establish the relationship between link weights, betweenness, and disorder strength (alpha).

Main Methods:

  • Analysis of the 'transport overlay network' formed by the union of all shortest path trees.
  • Examination of link betweenness (Bl) in various tree structures, including minimum spanning trees (MSTs) from different network models and real-world complex networks.
  • Investigation of betweenness distributions across different disorder regimes, controlled by the extreme value index (alpha) of link weights.

Main Results:

  • In the strong disorder limit (alpha -> 0), network transport concentrates on the MST, exhibiting a power-law betweenness distribution Pr[Bl=j] ~ j^(-c).
  • The exponent 'c' of the power-law distribution is positively correlated with the degree variance of the tree and independent of network size (N).
  • In the weak disorder regime, a negative correlation exists between link weight and betweenness, influenced by alpha and network topology.

Conclusions:

  • The betweenness distribution in overlay networks, particularly in the strong disorder limit, is robustly power-law across diverse tree topologies and degree distributions.
  • Link betweenness and traffic flow are fundamentally shaped by the interplay between network topology, disorder strength, and link weights.
  • Findings provide insights into traffic localization and the critical role of the MST in highly disordered networks.