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原文連結
論文資訊
- 類型：已發表論文
- 日期：2012
摘要
Understanding what types of phenomena lead to discontinuous 相變s in the connectivity of random 網絡s is an outstanding challenge. Here we show that a simple 隨機 model of graph 演化 leads to a discontinuous 滲流 transition and we derive the underlying mechanism responsible: growth by overtaking. Starting from a collection of n isolated nodes, potential edges chosen uniformly at random from the complete graph are examined one at a time while a cap, k, on the maximum allowed component size is enforced. Edges whose addition would exceed k can be simply rejected provided the accepted fraction of edges never becomes smaller than a function which decreases with k as g(k) = 1/2 + (2k)(-beta). We show that if beta < 1 it is always possible to reject a sampled edge and the growth in the largest component is
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