Abstract

We study first-order zero–one law and the first-order convergence law for two recursive random graph models, namely, the uniform and preferential attachment models. In the uniform attachment model, a new vertex with \(m\) edges chosen uniformly is added at every moment, while, in the preferential attachment model, the distribution of second ends of these edges is not uniform, but rather the probabilities are proportional to the degrees of the respective vertices.

中文翻译：

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递归随机图模型一阶句子概率的收敛性

摘要

我们研究了两个递归随机图模型（即统一和优先依恋模型）的一阶零一定律和一阶收敛定律。在均匀附着模型中，每时每刻都添加一个具有\（m \）个边缘均匀选择的新顶点，而在优先附着模型中，这些边缘的第二端的分布不是均匀的，而是概率成比例的到各个顶点的角度。