广义稠密随机交集图的度分布(英文)

广义随机交集图是一类重要的随机图模型,它是E-R随机图的变种,被广泛用于复杂社会网络的研究中.本文研究了在顶点度的期望趋于无穷的情况下,广义随机交集图的度分布.我们对二项模型给出了中心极限定理,并且对一致模型给出了极限定理.

Typical Vertex Degrees in Dense Generalized Random Intersection Graphs

.A generalized random intersection graph is constructed by independently assigning each vertex a random subset of a list of objects,and drawing an edge between two vertices if and only if their respective subsets intersect.In this paper,we study typical vertex degrees in generalized random intersection graphs when the expected degree tends to infinity,i.e.in the dense limiting regime.We present a central limit theorem for the degree of a typical vertex,and as a special case applying to the binomial model,our result improves a previous theorem.In addition,a strong law for the degree of a typical vertex is given in the uniform model.