On fast computation of directed graph Laplacian pseudo-inverse

被引：2
|
作者：
Boley, Daniel [1 ]
机构：
[1] Univ Minnesota, Minneapolis, MN 55455 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 623卷
基金：
美国国家科学基金会;
关键词：
Graph Laplacian; Directed graphs; Pseudo-inverse; Iterative methods; ALGORITHMS; GMRES;
D O I：
10.1016/j.laa.2020.10.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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. (C) 2020 Elsevier Inc. All rights reserved.
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页码：128 / 148
页数：21
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