论文标题
无尺度随机图中集团的渐近学
Asymptotics for cliques in scale-free random graphs
论文作者
论文摘要
在本文中，我们为Chung-lu不均匀的随机图模型中的预期集团数量建立了渐近学（随着图的大小增长到无穷大），其中为具有尾部概率$ h^{1-α} l（H）$的独立权重分配了顶点，其中$ h^{1-α} l（h）$，其中$α> 2 $ and $α> 2 $ and $ l $是一个缓慢的vary vary vary n。每对顶点通过边缘连接，概率与这些顶点的重量的乘积成正比。我们为所有集团尺寸和所有非全能$α> 2 $提供了一组完整的渐近学。我们还解释了为什么整数$α$不同的情况是不同的，在这种情况下，渐近药的部分结果。
In this paper we establish asymptotics (as the size of the graph grows to infinity) for the expected number of cliques in the Chung--Lu inhomogeneous random graph model in which vertices are assigned independent weights which have tail probabilities $h^{1-α}l(h)$, where $α>2$ and $l$ is a slowly varying function. Each pair of vertices is connected by an edge with a probability proportional to the product of the weights of those vertices. We present a complete set of asymptotics for all clique sizes and for all non-integer $α> 2$. We also explain why the case of an integer $α$ is different, and present partial results for the asymptotics in that case.
