Fontanelli Oscar, Hernández Demian, Mansilla Ricardo
Centro de Investigaciones Interdisciplinarias en Ciencias y Humanidades, UNAM, Mexico City, Mexico.
Facultad de Ciencias, UNAM, Mexico City, Mexico.
Soc Netw Anal Min. 2022;12(1):29. doi: 10.1007/s13278-022-00861-4. Epub 2022 Feb 2.
In this work we introduce a simple mathematical model, based on master equations, to describe the time evolution of the popularity of hashtags on the Twitter social network. Specifically, we model the total number of times a certain hashtag appears on user's timelines as a function of time. Our model considers two kinds of components: those that are internal to the network (degree distribution) as well as external factors, such as the external popularity of the hashtag. From the master equation, we are able to obtain explicit solutions for the mean and variance and construct confidence regions. We propose a gamma kernel function to model the hashtag popularity, which is quite simple and yields reasonable results. We validate the plausibility of the model by contrasting it with actual Twitter data obtained through the public API. Our findings confirm that relatively simple semi-deterministic models are able to capture the essentials of this very complex phenomenon for a wide variety of cases. The model we present distinguishes from other existing models in its focus on the time evolution of the total number of times a particular hashtag has been seen by Twitter users and the consideration of both internal and external components.
在这项工作中，我们引入了一个基于主方程的简单数学模型，以描述推特社交网络上主题标签热度随时间的演变。具体而言，我们将某个主题标签在用户时间线上出现的总次数建模为时间的函数。我们的模型考虑了两种成分：网络内部的成分（度分布）以及外部因素，例如主题标签的外部热度。从主方程中，我们能够获得均值和方差的显式解，并构建置信区域。我们提出了一个伽马核函数来对主题标签热度进行建模，该函数相当简单且能产生合理的结果。我们通过将其与通过公共应用程序编程接口获取的实际推特数据进行对比，来验证该模型的合理性。我们的研究结果证实，相对简单的半确定性模型能够在多种情况下捕捉到这一非常复杂现象的本质。我们提出的模型与其他现有模型的不同之处在于，它关注推特用户看到特定主题标签的总次数的时间演变，并考虑了内部和外部成分。
