TY - JOUR
TI - Graphs with absorption: Numerical methods for the absorption inverse and the computation of centrality measures
AU - Benzi, M.
AU - Fika, P.
AU - Mitrouli, M.
JO - LINEAR ALGEBRA AND ITS APPLICATIONS
PY - 2019
VL - 574
TODO - null
SP - 123-152
PB - W B SAUNDERS CO-ELSEVIER INC
SN - 0024-3795
TODO - 10.1016/j.laa.2019.03.026
TODO - Graphic methods;  Inverse problems;  Iterative methods;  Numerical methods, Centrality measures;  Group inverse;  Krylov subspace method;  Laplacian matrices;  Matrix factorizations;  Preconditioning, Matrix algebra
TODO - The absorption inverse, studied in Jacobsen and Tien (2018) [13], is a generalized inverse specifically introduced for the analysis of graphs with absorption. In this paper we consider numerical methods for the efficient computation of the absorption inverse and related quantities. Both direct and iterative methods are developed. We also consider different centrality measures for graphs with absorption, as well as fast updating/downdating techniques. Numerical experiments show that computations on graphs with up to 36 million edges can be performed quickly on a standard laptop. © 2019 Elsevier Inc.
ER -