The Degree Distribution of Networks: Statistical Model Selection

The degree distribution has been viewed as an important characteristic of network data. Many biological networks have been labelled scale-free as their degree distribution can be approximately described by a power-law probability distribution. This chapter presents a formal statistical model selection procedure that can determine which functional form, from a collection of specified models, best describes the degree distribution of network data. The degree distribution found for empirical data is viewed as belonging to a class of probability models and the model which best describes the data is determined in a maximum likelihood framework. In conclusion, it is important to note that these statistical tests do not confirm the true underlying distribution of the observed data, but instead show which models from a chosen set best describe the data. In reality, these approaches should be viewed as providing evidence for which probability models do not adequately (or optimally) describe the data, and give an indication of the underlying sampling and true interaction properties of the system considered.