Abstract
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.
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Acknowledgement
The authors thank Clarivate Analytics to provide the access to the raw data of the Web of Science database for research investigations via the international collaboration between the Institute of Statistical Mathematics (ISM) of Japan and the Institute of Statistical Science, Academia Sinica (ISSAS) of Taiwan. The authors also thank Ms. Ula Tzu-Ning Kung for her service on English editing to improve the quality of this paper. This work was supported partially by the thematic project (ASCEND) of Academia Sinica (Taiwan) grant number AS-109-TP-M07 and the Ministry of Science and Technology (Taiwan) grant numbers 107-2118-M-001-011-MY3 and 109-2321-B-001-013.
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Jung, H., Phoa, F.K.H. (2021). Analysis of a Finite Mixture of Truncated Zeta Distributions for Degree Distribution. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications IX. COMPLEX NETWORKS 2020 2020. Studies in Computational Intelligence, vol 944. Springer, Cham. https://doi.org/10.1007/978-3-030-65351-4_40
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