Abstract
The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often 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 behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.
Highlights
Network science focuses on the study of complex networks such as telecommunication, computer, biological, cognitive, and social networks
We propose a mixture model of truncated zeta distributions for the analysis of degree distributions
We focus on analyzing actual scientific collaboration networks and have made significant advancements compared to the previous work in Jung and Phoa (2020) [32]
Summary
This paper is an extended version of our paper published in Jung, H.; Phoa, F.K.H. Analysis of a Finite. Mixture of Truncated Zeta Distributions for Degree Distribution. Conference on Complex Networks and Their Applications, Madrid, Spain, 1–3 December 2020; pp. Conference on Complex Networks and Their Applications, Madrid, Spain, 1–3 December 2020; pp. 497–507
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