【作者】 李莉；

【导师】 耿显民；

【作者基本信息】 南京航空航天大学 ， 概率论与数理统计， 2014， 硕士

【摘要】 现实世界中许多复杂系统都可以通过复杂网络进行描述，近年来国内外掀起了复杂网络研究热潮。网络的拓扑结构和网络行为间的密切关系，使得复杂网络性质的形成机制成为人们研究的焦点。许多实证研究表明，无标度性、大团聚性是复杂网络的重要特性。然而，团聚系数的数学刻画是复杂网络研究的一个难点，至今尚未得到有效的计算团聚系数的数学表达式。为了准确描述复杂网络团聚系数，我们研究了一类具有集聚连接和度偏好连接的网络演化模型。本文研究的网络演化模型中，每一操作步增加一个带两条边的新结点到网络中，两条边分别以集聚连接和偏好连接的方式连接到当前网络。通过数学推导，给出了任意时刻结点的度、邻点度数和、邻点间边数及团聚系数，进而得到演化网络的度分布、团聚系数的精确表达式，最后通过与仿真模拟结果进行对比，验证了表达式的有效性。更多还原

【Abstract】 Many complex systems can be described by complex network. In recent years, the researchof complex network becomes popular. The close relation between the network topology andnetwork behavior makes the formation mechanism of complex network features become aresearch focus. Many empirical studies showed that scale-free behavior of the degree distributionand high clustering properties are important features of the complex network. However, themathematical characterization of the clustering coefficient is a difficulty of complex networkresearch, and there is no efficient mathematical expression to calculate the clustering coefficientyet.In order to describe the clustering coefficient of complex network, we investigate a class ofevolving network with clustering preferential connection and degree preferential attachment. Inthis model, at each operation step, a new node with two edges is added into the network, and itstwo edges are linked to the previous network by clustering preferential connection and degreepreferential attachment respectively. By mathematical derivation, the degree, the sum ofneighbors’ degree and the number of edges between neighbors of an arbitrary node at time t and itsclustering coefficient are obtained. Based on these, the degree distribution and the accurateexpression of clustering coefficient of evolving network are given as well. Then, we illustrate thatthe clustering coefficient expression is consistent with the simulation result.更多还原