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.

Graphs with absorption: Numerical methods for the absorption inverse and the computation of centrality measures

Benzi, Michele;FIKA, Paraskevi;
2019

Abstract

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
Settore MAT/08 - Analisi Numerica
Absorption inverse; Centrality measure; Group inverse; Krylov subspace methods; Laplacian matrix; Matrix factorizations; Preconditioning; Algebra and Number Theory; Numerical Analysis; Geometry and Topology; Discrete Mathematics and Combinatorics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79305
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