This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the modularity matrix, and we derive the error of the approximation. There is also a complete proof of the equivalence between normalized adjacency clustering and normalized modularity clustering. Numerical experiments show that normalized adjacency clustering can be as twice efficient as normalized modularity clustering.

翻译：本文建立了非归一化模块度矩阵的主特征向量与邻接矩阵特征向量之间的精确线性关系。我们提出了一种近似模块度矩阵主特征向量的方法，并推导了该近似的误差。同时，本文完整证明了归一化邻接聚类与归一化模块度聚类之间的等价性。数值实验表明，归一化邻接聚类的效率可达到归一化模块度聚类的两倍。