Social Networks Count Data: Negative Binomial Distributions and Extensions Versus Poisson and Bernoulli Models

With the development of the modern Internet, the use of social networks has increased significantly, which has promoted the research on social network analysis models in modern times. However, the modern academic community lacks a systematic integration and analysis of the selection of social network models, making it difficult for researchers and practitioners to choose a suitable model according to the actual situation of their research. This study aims to explain the advantages and disadvantages of four social network models (Bernoulli, Poisson, negative binomial, and zero-inflated) and systematically illustrate which model is suitable for which social network analysis through mathematical calculations and tabular organization. This paper concludes that in binary analysis and traditional analysis, the Bernoulli distribution and Poisson distribution are suitable for explaining such simple social networks. However, as the complexity of social networks increases, when complex conditions such as the proliferation of zero values and overdispersion are added, the shortcomings of simple models are revealed, which the more complex negative binomial model and zero-inflated model can well calculate and analyze social networks. This study provides a systematic model selection strategy for future researchers, but it lacks the analysis of dynamic multi-model social networks and mainly focuses on models of static networks. Therefore, future researchers can focus on analyzing the application of more complex models in dynamic networks and their advantages and disadvantages.