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A unifying framework for fast randomization of ecological networks with fixed (node) degrees.

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The Curveball algorithm efficiently randomizes bipartite networks. New extensions now allow unbiased randomization for directed and undirected networks, ensuring uniform sampling of configurations.

Keywords:
Binary matricesCo-occurrenceCurveball algorithmFood webNull model

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Area of Science:

  • Network science
  • Graph theory
  • Computational mathematics

Background:

  • Randomizing networks while preserving node degrees is crucial for statistical analysis.
  • The original Curveball algorithm efficiently randomizes bipartite networks.
  • Existing methods may lack efficiency or unbiasedness for certain network types.

Purpose of the Study:

  • To extend the Curveball algorithm for randomizing unimode directed and undirected networks.
  • To ensure the extended algorithms are both efficient and unbiased.
  • To provide mathematical validation for the new randomization procedures.

Main Methods:

  • Development of two novel extensions to the Curveball algorithm.
  • Application of formal mathematical proofs to verify algorithm properties.
  • Analysis of network configurations and sampling uniformity.

Main Results:

  • The two extensions successfully randomize unimode directed and undirected networks.
  • Both extensions maintain the efficiency and unbiasedness of the original Curveball algorithm.
  • Mathematical proofs confirm uniform sampling from the space of possible network configurations.

Conclusions:

  • The extended Curveball algorithm provides a robust tool for network randomization across various network types.
  • These advancements facilitate more accurate statistical inference in network analysis.
  • The unbiased and efficient nature of the algorithm is mathematically guaranteed.