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

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.