应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2010年
4期
767-773
,共7页
交集图%随机图%度分布%中心极限定理
交集圖%隨機圖%度分佈%中心極限定理
교집도%수궤도%도분포%중심겁한정리
Intersection graphs%Random graphs%Degree%Central limit theorem
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.
廣義隨機交集圖是一類重要的隨機圖模型,它是E-R隨機圖的變種,被廣汎用于複雜社會網絡的研究中.本文研究瞭在頂點度的期望趨于無窮的情況下,廣義隨機交集圖的度分佈.我們對二項模型給齣瞭中心極限定理,併且對一緻模型給齣瞭極限定理.
엄의수궤교집도시일류중요적수궤도모형,타시E-R수궤도적변충,피엄범용우복잡사회망락적연구중.본문연구료재정점도적기망추우무궁적정황하,엄의수궤교집도적도분포.아문대이항모형급출료중심겁한정리,병차대일치모형급출료겁한정리.
.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.
