通过具有扩展颜色的波利亚瓮生成优先附着图

IF 1.4 Q2 SOCIAL SCIENCES, INTERDISCIPLINARY Network Science Pub Date : 2024-04-08 DOI:10.1017/nws.2024.3
Somya Singh, Fady Alajaji, Bahman Gharesifard
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引用次数: 0

摘要

我们介绍了一种新颖的优先依附模型,该模型使用了颜色数量不断增加的改良波利亚瓮的绘制变量,随着图的演化,该模型能够对有影响力的意见(以高度数顶点为单位)进行建模。与巴拉巴西-阿尔伯特模型类似,生成的图在每个时间实例中都会增加一个顶点;但与此不同的是,图中的每个顶点都有一种颜色,这种颜色由波利亚瓮中的球色表示。更具体地说,在每个时间步长内,我们都会从瓮中抽出一个球,并将其与若干相同颜色的强化球一起放回瓮中;我们还会向瓮中添加另一个新颜色的球。然后,我们会在新顶点(对应新颜色)和现有顶点(其颜色球已被提取)之间构建一条边。将颜色编码顶点与随时间变化的强化参数结合使用,可以使在此过程中较晚添加(诞生)的顶点有可能达到较高的度数,而这是巴拉巴西-阿尔伯特模型无法捕捉到的。我们通过分析基本随机过程的抽取向量来研究顶点的度数。特别是,我们建立了随机变量的概率分布,该随机变量计算特定颜色的抽签次数,而抽签次数决定了图中与该颜色对应的顶点的度数。我们还提供了模拟结果,对我们的模型和巴拉巴西-阿尔伯特网络进行了比较。
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Generating preferential attachment graphs via a Pólya urn with expanding colors
We introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.
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来源期刊
Network Science
Network Science SOCIAL SCIENCES, INTERDISCIPLINARY-
CiteScore
3.50
自引率
5.90%
发文量
24
期刊介绍: Network Science is an important journal for an important discipline - one using the network paradigm, focusing on actors and relational linkages, to inform research, methodology, and applications from many fields across the natural, social, engineering and informational sciences. Given growing understanding of the interconnectedness and globalization of the world, network methods are an increasingly recognized way to research aspects of modern society along with the individuals, organizations, and other actors within it. The discipline is ready for a comprehensive journal, open to papers from all relevant areas. Network Science is a defining work, shaping this discipline. The journal welcomes contributions from researchers in all areas working on network theory, methods, and data.
期刊最新文献
Guiding prevention initiatives by applying network analysis to systems maps of adverse childhood experiences and adolescent suicide The latent cognitive structures of social networks Algorithmic aspects of temporal betweenness When can networks be inferred from observed groups? Generating preferential attachment graphs via a Pólya urn with expanding colors
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