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Thresholding normally distributed data creates complex networks.

George T Cantwell1, Yanchen Liu2, Benjamin F Maier3,4

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.

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Summary
This summary is machine-generated.

Thresholding correlated data generates networks with complex network properties like heavy tails and short paths. However, this simple model does not fully replicate complex network characteristics such as clustering or community structure.

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Area of Science:

  • Network Science
  • Data Analysis
  • Statistical Modeling

Background:

  • Network datasets often arise from thresholding procedures.
  • Resulting networks commonly exhibit properties like heavy-tailed degree distributions, clustering, large connected components, and short average shortest path lengths.
  • These characteristics are frequently associated with complex networks and their universality is often considered.

Purpose of the Study:

  • To introduce a simple model for correlated relational data.
  • To investigate the network ensemble generated by thresholding this correlated data.
  • To determine which complex network properties emerge from this simplified model.

Main Methods:

  • Development of a simple model for correlated relational data.
  • Application of a thresholding procedure to the model's data.
  • Analysis of the resulting network ensemble for characteristic properties.

Main Results:

  • Thresholding correlated data yields networks with heavy-tailed degree distributions.
  • A significant number of triangles are observed in the generated networks.
  • Short path lengths are a notable feature of the resulting network structures.
  • Nonvanishing clustering and community structure were not observed.

Conclusions:

  • The study demonstrates that thresholding correlated data can reproduce some, but not all, complex network properties.
  • Heavy-tailed distributions, triangles, and short paths emerge even when the underlying data lacks inherent complexity.
  • The model highlights the limitations of thresholding in generating all hallmarks of complex networks, particularly clustering and community structure.