Robust Analysis of Preferential Attachment Models with Fitness
Robust Analysis of Preferential Attachment Models with Fitness
复制标题
具有适应度的偏好依恋模型的鲁棒分析
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Marcel Ortgiese
中科院分区：
文献类型：
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作者：
S. Dereich;Marcel Ortgiese
具有适应度的偏好连接网络是一个动态随机图模型。新的顶点被连续引入，新的顶点被连接到旧的顶点，其概率与旧的顶点的度乘以随机适应度成正比。我们集中在典型的行为的图形计算的健身分布的顶点选择成比例的程度。对于模型的一个特定变体，这种分析首先由Borgs，Chayes，Daskalakis和Roch进行。然而，我们提出了一种新的方法，这是强大的意义上说，它不依赖于确切的规格的附件法。特别是，我们表明，一种特殊的现象，被称为玻色-爱因斯坦凝聚，可以观察到各种各样的模型。最后，我们还计算了一个统一选择的顶点的联合度和适应度分布。
The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied by a random fitness. We concentrate on the typical behaviour of the graph by calculating the fitness distribution of a vertex chosen proportional to its degree. For a particular variant of the model, this analysis was first carried out by Borgs, Chayes, Daskalakis and Roch. However, we present a new method, which is robust in the sense that it does not depend on the exact specification of the attachment law. In particular, we show that a peculiar phenomenon, referred to as Bose–Einstein condensation, can be observed in a wide variety of models. Finally, we also compute the joint degree and fitness distribution of a uniformly chosen vertex.