论文标题
小世界网络的特征向量的多重分析
Multifractal analysis of eigenvectors of smallworld networks
论文作者
论文摘要
许多现实世界中的复杂系统具有小世界拓扑结构，其特征是节点的高聚类和短路径长度。众所周知，较高的聚类驱动定位，而较短的路径长度支持网络特征向量的定位。我们使用多型技术技术研究了使用Watts-Strogatz算法构建的小世界网络邻接矩阵的特征向量的定位属性。我们发现特征值光谱的中心部分的特征是强多纹状体，而光谱的尾部部分具有dq-> 1。在小世界转变开始之前，随机连接的增加导致特征向量定位的增强，而在开始后，特征向量显示了本地化的逐渐减少。我们已经验证了在本地化范围过渡时相关维度的急剧变化
Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the eigenvectors of the adjacency matrices of small-world networks constructed using Watts-Strogatz algorithm. We find that the central part of the eigenvalue spectrum is characterized by strong multifractality whereas the tail part of the spectrum have Dq->1. Before the onset of the small-world transition, an increase in the random connections leads to an enhancement in the eigenvectors localization, whereas just after the onset, the eigenvectors show a gradual decrease in the localization. We have verified an existence of sharp change in the correlation dimension at the localization-delocalization transition
