论文标题
在随机图中具有指定度序列的对称阈值
The threshold of symmetry in random graphs with specified degree sequences
论文作者
论文摘要
我们提供了足够的条件，在该条件下，具有指定度序列的随机图是对称或不对称的。在有界度序列的情况下，我们的表征捕获了随机图的对称性的相变。该相变与图形连接的相吻合。但是，当最高程度是增长的功能，因为顶点趋于无穷大，我们的结果表明，这两个阈值不再重合
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random graphs. This phase transition coincides with that of the graph connectivity. However, when the maximum degree is a growing function as the number of vertices tends to infinity, our results suggest that these two thresholds do not coincide any more
