The 3-cycle weighted spectral distribution in evolving community-based networks
The 3-cycle weighted spectral distribution in evolving community-based networks
复制标题
不断发展的基于社区的网络中的 3 周期加权谱分布
DOI：
10.1063/1.4978024
复制
发表时间：
2017-03-01
期刊：
影响因子：
2.9
通讯作者：
Wu, Xiaoqun
中科院分区：
文献类型：
--
作者：
Jiao, Bo;Wu, Xiaoqun
现实世界网络中的主要组织原则之一是网络社区，其中节点集合组织成密集连接的集群。这些基于社区的网络中有许多是随着时间的推移而发展的，也就是说，我们需要一些与大小无关的指标来捕捉这些集群中嵌入的连接关系。其中一个指标是平均聚类系数，它代表了网络中所有节点之间的三角关系。然而，绝大多数网络社区是由低度节点组成的。因此，我们应该进一步研究其他与大小无关的度量，以微妙地衡量低度节点之间的三角关系。在本文中，我们研究了3圈加权谱分布（WSD），它被定义为具有缩放因子n的归一化拉普拉斯谱分布的加权和，其中n是网络规模（即，节点编号）。使用一些历时的基于社区的网络模型和现实世界的网络，我们证明了3圈WSD的网络规模的比率是渐近独立的网络规模，并严格表示低度节点之间的三角关系。此外，我们发现，该比率是一个很好的指标的平均聚类系数在不断发展的社区为基础的系统。由AIP出版社出版。
One of the main organizing principles in real-world networks is that of network communities, where sets of nodes organize into densely linked clusters. Many of these community-based networks evolve over time, that is, we need some size-independent metrics to capture the connection relationships embedded in these clusters. One of these metrics is the average clustering coefficient, which represents the triangle relationships between all nodes of networks. However, the vast majority of network communities is composed of low-degree nodes. Thus, we should further investigate other size-independent metrics to subtly measure the triangle relationships between low-degree nodes. In this paper, we study the 3-cycle weighted spectral distribution (WSD) defined as the weighted sum of the normalized Laplacian spectral distribution with a scaling factor n, where n is the network size (i.e., the node number). Using some diachronic community-based network models and real-world networks, we demonstrate that the ratio of the 3-cycle WSD to the network size is asymptotically independent of the network size and strictly represents the triangle relationships between low-degree nodes. Additionally, we find that the ratio is a good indicator of the average clustering coefficient in evolving community-based systems. Published by AIP Publishing.