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A preferential attachment process approaching the Rado graph
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2020-02-27 , DOI: 10.1017/s0013091519000336 Richard Elwes
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2020-02-27 , DOI: 10.1017/s0013091519000336 Richard Elwes
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 d u (t )/t , where d u (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。
更新日期:2020-02-27
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 (