We consider a simple preferential attachment graph process, which begins with a finite graph and in which a new (t + 1)st vertex is added at each subsequent time step t that is connected to each previous vertex u ≤ t with probability du(t)/t, where du(t) is the degree of u at time t. We analyse the graph obtained as the infinite limit of this process, and we show that, as long as the initial finite graph is neither edgeless nor complete, with probability 1 the outcome will be a copy of the Rado graph augmented with a finite number of either isolated or universal vertices.

中文翻译：

---

接近 Rado 图的优先依附过程

我们考虑一个简单的优先依附图过程，它从一个有限图开始，其中一个新的 (吨+ 1) 在每个后续时间步添加第一个顶点吨连接到每个先前的顶点你≤吨有概率d你(吨)/吨， 在哪里d你(吨) 是程度你有时吨. 我们分析作为该过程的无限极限获得的图，并且我们表明，只要初始有限图既不是无边也不是完整的，以概率 1，结果将是 Rado 图的副本，增加了有限数量的孤立的或通用的顶点。