Structure and dynamics of human disease-complication network

Jiang, Xiong-Fei; Xiong, Long; Bai, Ling; Lin, Jie; Zhang, Jingfeng; Yan, Kun; Zhu, Jun; Zheng, Bin; Zheng, Jianjun

doi:10.1101/2021.12.13.472342

Cited by 1 publication

(1 citation statement)

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“…Empirical studies in the last two decades on real-world complex networks such as collaboration, communication, social, biological, and temporal networks are assumed to follow a power law distribution [10], [13], [20]- [22]. Consequently, scale-free complex networks are recently used as an essential substrate for studying many other facts in network science, such as human interaction [23], [24], COVID-19 pandemic [25], [26], and information diffusion [27], [28] among many others.…”

Section: Introductionmentioning

confidence: 99%

Searching for Heavy-Tailed Probability Distributions for Modeling Real-World Complex Networks

et al. 2022

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Perhaps the most recent controversial topic in network science research is to determine whether real-world complex networks are scale-free or not. Recently, Broido and Clauset [A.D. Broido, A. Clauset, Nature Communication, 10, 1017 (2019)] asserted that the degree distributions of real-world networks are rarely power law under statistical tests. Such complex networks, including social, biological, information, temporal, and brain networks, are often heavy-tailed where the assumption on the scale-free nature of real-world heavy-tailed networks become insignificant as the complex system evolves over time. The failure of power law distribution in fitting the degree distribution data is mainly due to the presence of an identifiable non-linearity within the entire degree distribution in a log-log scale of a complex heavytailed network. In this study, we attempt to address this issue by proposing a new class of heavy-tailed probability distributions for modeling the entire degree distributions of complex networks. We introduce a new family of generalized Lomax models (GLM) to capture the non-linearity of these heavy-tailed networks. These newly introduced GLM-type distributions provide better fitting and greater flexibility to the entire node degree distribution of complex networks. Several statistical properties of the proposed model, such as extreme value and inferential statistical properties, are derived into this context. Interestingly, the GLM family belongs to the basin of attraction of Frechet distribution, a heavy-tailed extreme value distribution. Rigorous experimental analysis showcases the excellent performance of the proposed family of distributions while fitting the heavy-tailed real-world complex networks over fifty real-world datasets in comparison with benchmark probability models. Our results show that GLM-type distributions are not rare, able to model almost 90% of the tested networks accurately compared to benchmark probability models.

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