邻接与模块度图划分之间的关系
Relations Between Adjacency and Modularity Graph Partitioning
AI总结：
本文揭示邻接矩阵与模块度矩阵特征向量的精确线性关系，提出主导特征向量近似并推导误差，证明两类归一化聚类等价，且实验显示邻接聚类效率可达两倍。
摘要：
本文建立了非归一化模块度矩阵的主导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导特征向量的方法，并推导了该近似的误差。文中还给出了归一化邻接聚类与归一化模块度聚类等价性的完整证明。数值实验表明，归一化邻接聚类的效率可达归一化模块度聚类的两倍。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
