论文标题
关于幂律随机图的评论
Remarks on power-law random graphs
论文作者
论文摘要
图形理论是理解大型网络属性的重要工具。我们研究了一个随机图模型，并将其施放在Graphon框架中。限制图的独特结构在亚临界和超临界方案中进行了详细探讨。在亚临界策略中，该图是空的，概率很高，在极少数情况下，它是非空的，它由单个边缘组成。相反，在超临界状态中，存在非平凡的随机图，它是不同类型的图形收敛之间未覆盖的边界情况。
The theory of graphons is an important tool in understanding properties of large networks. We investigate a power-law random graph model and cast it in the graphon framework. The distinctively different structures of the limit graph are explored in detail in the sub-critical and super-critical regimes. In the sub-critical regime, the graph is empty with high probability, and in the rare event that it is non-empty, it consists of a single edge. Contrarily, in the super-critical regime, a non-trivial random graph exists in the limit, and it serves as an uncovered boundary case between different types of graph convergence.
