Detection of degree distribution for biological networks in pearson family and its approximation

The degree distribution is one of the characteristic features of the topology of networks. This distribution describes the in-degree and out-degree of nodes in systems. In genetic networks, the in-degree or arriving connectivity represents the number of links coming to a target gene, while the out-degree or departing connectivity represents the number of links leaving the target gene. For biological networks, the in-degree distribution can be modeled by the exponential distribution, whereas the power-law distribution generally models the out-degree distribution. However, truncated power-law, generalized Pareto, stretched exponential, geometric, or combinations of these distributions may serve as robust alternative out-degree models, satisfying the centrality and small-world properties even without scale-free behavior. The Pearson curve is a fundamental tool for categorizing distributions based on the characteristics of their first four moments. In this study, we aim to describe the out-degree of biological systems through an alternative approach. This approach ensures that the previously mentioned out-degree densities are treated as special cases within the Pearson curve framework. Their distributional similarities are evaluated using the three-moment Chi-square and four-moment F approximations. As a result, we assess the effectiveness of our proposed method in accurately classifying these distributions. The findings reveal that the degree distributions satisfying the scale-free property mainly fall within the Pearson Type I family, with only a few in Type VI. In contrast, clustered and hub networks do not align with Pearson distributions. The scale-free networks demonstrate the applicability of the four-moment F approximation, highlighting the robustness of Pearson curves in modeling biological networks. This study suggests that fitting a plausible distribution in the Pearson families provides realistic choices for the degree distribution in biological networks, addressing limitations in existing methodologies and opening pathways for further research on various biological network types and distribution systems.