The Zipf-Polylog distribution: Modeling human interactions through social networks

Valero, Jordi; Pérez-Casany, Marta; Duarte-López, Ariel

doi:10.1016/j.physa.2022.127680

Cited by 7 publications

(5 citation statements)

References 26 publications

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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%

“…For example, Corral and Gonzalez (2019) elucidated the range of validity of the power law with its corresponding exponent and improved power law tail using a truncated lognormal distribution to study geoscience phenomena [36]. In another work, the Zipf-Polylog family of distributions was proposed by [23] for analyzing the degree sequence of two complex real-world networks in all its range. More recently, a study on Virus spread based on a scale-free network reproduced the Gompertz growth observed in isolated COVID-19 outbreaks [26].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…In particular, this is the only extension that is a two-parameter exponential family and that has moments of any order regardless of the parameter values. The results related to this family appear in Valero et al [2020].…”

Section: Introductionmentioning

confidence: 88%

“…At the end we include a section devoted to the analysis of random data generation from the Zipf-Polylog distribution. Most of the work presented in this chapter is included in the paper "The Zipf as a Mixture Distribution and Its Polylogarithm Generalization" [Valero et al, 2020], which at the moment of writing this PhD thesis is under revision.…”

Section: Chaptermentioning

confidence: 99%

Zipf extensions and their applications for modeling the degree sequences of real networks

Duarte López

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The Zipf distribution, also known as discrete Pareto distribution, attracts considerable attention because it helps describe skewed data from many natural as well as man-made systems. Under the Zipf distribution, the frequency of a given value is a power function of its size. Consequently, when plotting the frequencies versus the size in log-log scale for data following this distribution, one obtains a straight line. Nevertheless, for many data sets the linearity is only observed in the tail and when this happens, the Zipf is only adjusted for values larger than a given threshold. This procedure implies a loss of information, and unless one is only interested in the tail of the distribution, the need to have access to more flexible alternatives distributions is evidenced. The work conducted in this thesis revolves around four bi-parametric extensions of the Zipf distribution. The first two belong to the class of Random Stopped Extreme distributions. The third extension is the result of applying the concept of Poisson-Stopped-Sum to the Zipf distribution and, the last one, is obtained by including an additional parameter to the probability generating function of the Zipf. An interesting characteristic of three of the models presented is that they allow for a parameter interpretation that gives some insights about the mechanism that generates the data. In order to analyze the performance of these models, we have fitted the degree sequences of real networks from different areas as: social networks, protein interaction networks or collaboration networks. The fits obtained have been compared with those obtained with other bi-parametric models such as: the Zipf-Mandelbrot, the discrete Weibull or the negative binomial. To facilitate the use of the models presented, they have been implemented in the zipfextR package available in the Comprehensive R Archive Network. La distribución Zipf, también conocida como distribución discreta de Pareto, atrae una atención considerable debido a su versatilidad para describir datos sesgados provenientes de diferentes entornos tanto naturales como artificiales. Bajo la distribución Zipf, la probabilidad de un valor dado es proporcional a una potencia negativa del mismo. En consecuencia, al dibujar en escala doble logarítmica las frecuencias, de datos provenientes de esta distribución, en función de su tamaño, se obtiene una línea recta. Sin embargo, en muchos conjuntos de datos, esta linealidad solo se observa en la cola, y cuando esto sucede, la distribución Zipf solo se ajusta para valores mayores que un umbral dado. Este procedimiento implica una pérdida de información, y a menos que a uno solo le interese la cola de la distribución, se pone de manifiesto la necesidad de disponer de distribuciones alternativas con una mayor flexibilidad. El trabajo realizado en esta tesis gira en torno a cuatro extensiones bi-paramétricas de la distribución Zipf. Las dos primeras pertenecen a la familia de distribuciones Random Stopped Extreme. La tercera extensión es el resultado de aplicar el concepto Poisson-Stopped-Sum a la distribución Zipf y, la última familia de distribuciones se obtiene al incluir un parámetro adicional a la función generadora de probabilidad de la Zipf. Una característica de tres de los modelos presentados es que proporcionan una interpretación directa de sus parámetros, lo que permite extraer algunas ideas sobre el mecanismo subyacente que ha generado los datos. Con el objetivo de analizar la aplicabilidad de estos modelos, hemos ajustado secuencias de grados de redes reales de diferentes áreas tales como: redes sociales, redes de interacción de proteínas y redes de colaboración. Los ajustes obtenidos se han comparado con los obtenidos con otros modelos bi-paramétricos como: el Zipf-Mandelbrot, la distribución discreta de Weibull o la binomial negativa. Para facilitar el uso de los modelos presentados, estos se han implementado en el paquete de R zipfextR, disponible en el Comprehensive R Archive Network.

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“…For several decades, plentiful domains have engaged in quantitative examinations of Zipf's Law [28][29][30][31][32][33][34][35][36]. They perceive themselves as complex systems comprised of numerous individual objects whose behaviors interdepend and evolve dynamically, thus giving rise to emergent collective behaviors [37].…”

Section: Zipf's Lawmentioning

confidence: 99%

Commercialization of state-owned broadcast networks in China

Yan¹

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Visual contents, such as illustrations and images, play a big role in product manual understanding. Existing Product Manual Question Answering (PMQA) datasets tend to ignore visual contents and only retain textual parts. In this work, to emphasize the importance of multimodal contents, we propose a Multimodal Product Manual Question Answering (MPMQA) task. For each question, MPMQA requires the model not only to process multimodal contents but also to provide multimodal answers. To support MPMQA, a large-scale dataset PM209 is constructed with human annotations, which contains 209 product manuals from 27 well-known consumer electronic brands. Human annotations include 6 types of semantic regions for manual contents and 22,021 pairs of question and answer. Especially, each answer consists of a textual sentence and related visual regions from manuals. Taking into account the length of product manuals and the fact that a question is always related to a small number of pages, MP-MQA can be naturally split into two subtasks: retrieving most related pages and then generating multimodal answers. We further propose a unified model that can perform these two subtasks all together and achieve comparable performance with multiple task-specific models. The PM209 dataset is available at https://github.com/AIM3-RUC/MPMQA.

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The Zipf-Polylog distribution: Modeling human interactions through social networks

Cited by 7 publications

References 26 publications

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

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

Zipf extensions and their applications for modeling the degree sequences of real networks

Commercialization of state-owned broadcast networks in China

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