关于有向图Laplacian伪逆的快速计算
On Fast Computation of Directed Graph Laplacian Pseudo-Inverse
摘要：
强连通有向图的拉普拉斯矩阵及其伪逆矩阵是计算有向图许多性质的基础。示例包括随机游走中心性和介数度量、平均命中和通勤时间以及其他连接性度量。这些措施出现在许多社会和计算机网络的分析。在这篇简短的论文中，我们展示了如何解决一个线性系涉及拉普拉斯算子的时间线性的边缘数，倍的因素取决于图的可分性。这直接导致在节点数量的时间平方上的整个拉普拉斯伪逆的逐列计算，即，每个矩阵条目的恒定时间。该方法是基于“现成的”迭代法，全局线性收敛是有保证的，而不求助于任何矩阵消除算法。
英文摘要：
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and commute times, and other connectivity measures. These measures arise in the analysis of many social and computer networks. In this short paper, we show how a linear system involving the Laplacian may be solved in time linear in the number of edges, times a factor depending on the separability of the graph. This leads directly to the column-by-column computation of the entire Laplacian pseudo-inverse in time quadratic in the number of nodes, i.e., constant time per matrix entry. The approach is based on "off-the-shelf" iterative methods for which global linear convergence is guaranteed, without recourse to any matrix elimination algorithm.
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。
