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

Abstract

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.

Development of a Modified Method of Network Traffic Forming

“…The characteristics of the traffic generated by a single voice source are highly dependent on the language coder (codec) used. Most commonly, voice traffic can be viewed as a superposition of a large number of individual independent ON/OFF sources transmitting at the same intensity but with durations distributed according to a heavy-tailed distribution [2,8].…”

Learning Patterns from Biological Networks: A Compounded Burr Probability Model

“…Voitalov et al [38] demonstrated a close relationship between the scale-free property and the Pareto type-II or Lomax distribution. Some recent studies have demonstrated the use of Lomax [39], Burr [40], and other heavy-tailed distributions [41] for modeling real-world complex networks. Broido and Clauset [2] further noted that recent complex network datasets deviate from the power-law distribution, supporting earlier claims by [42].…”