Abstract: In general, the bisection spectral method always uses only one certain eigenvalue and its corresponding  eigenvector to extract communities, which does not guarantee to obtain the best community structures. To solve this problem, this paper proposes a bisection spectral method based on the optimal eigenvectors, which utilizes the eigenvectors of transition matrices to partition the network/subnetwork into communities repeatedly, and the eigenvector used in each partition is the one whose bisection can lead to the largest modularity increment. Besides this, in order to encode the topological information into the proposed method, this paper also converts the original networks into weighted ones by utilizing the information of common neighbors of the two end vertices associated with each edge. Based on the transition matrix of the converted network, this paper applies the same bisection spectral method to extract communities. The experiments on 7 real-world networks are performed, and the experimental results show that the proposed method can extract the high-quality community structures from networks effectively.

Key words: community detection, bisection spectral method, eigenvalues, eigenvector, modularity

摘要： 针对传统谱二分社团检测算法一般只使用某一特定的特征向量对网络进行划分，并不能保证能够得到最佳的社团结构这一缺陷，提出了一种使用最优特征向量的谱二分社团检测方法。该方法利用网络/子网络转移矩阵的特征向量持续将网络分裂为若干个子网络，分裂过程并不固定使用单一的、特定的特征向量，每次分裂使用的是能使得模块度增量最大的一个特征向量。此外，为了充分利用网络的拓扑信息，还利用网络中每条边所关联的两个顶点拥有的共同邻居的信息，将原始网络转换为带权的网络，并基于此带权网络的转移矩阵，使用最优特征向量持续将其划分为若干个子网络，得到其社团结构。为了验证这两种方法的有效性，在7个实际网络上进行了实验。实验结果证实，该方法能够有效地从网络中提取高质量的社团结构。

关键词: 社团检测, 谱二分法, 特征值, 特征向量, 模块度