The degree distribution of networks: statistical model selection

Area of Science:

• Network Science
• Statistical Modeling
• Computational Biology

Background:

• Degree distribution is a key network characteristic.
• Many biological networks are considered scale-free, approximated by power-law distributions.
• Identifying the correct distribution is crucial for network analysis.

Purpose of the Study:

• To present a formal statistical model selection procedure.
• To determine the best functional form for describing network degree distributions from a set of models.
• To aid in understanding underlying sampling and interaction properties of biological systems.

Main Methods:

• Utilizing a maximum likelihood framework.
• Comparing empirical degree distributions against a class of probability models.
• Implementing a formal statistical model selection procedure.

Main Results:

• The study provides a method to select the most appropriate model for network degree distributions.
• It highlights that statistical tests indicate which models best describe the data, not the true underlying distribution.
• The approach offers insights into inadequacies of certain probability models.

Conclusions:

• Statistical model selection is vital for accurate network data interpretation.
• The presented method helps in choosing models that optimally describe degree distributions.
• This aids in inferring system properties from network topology.