Analysis of a Finite Mixture of Truncated Zeta Distributions for Degree Distribution

The power-law distribution has been widely used to describe the degree distribution of a network, especially when the range of degree is large. However, the deviation from such behavior appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law nature in a small degree range while maintaining the scale-free nature of a network. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. We apply our method on scientific collaboration networks with remarkable interpretations.