Reduced Google matrix
K. M. Frahm, D. L. Shepelyansky

TL;DR
This paper introduces a reduced Google matrix $G_R$ inspired by quantum scattering theory to analyze interactions within a selected subset of nodes in large directed networks, accounting for indirect links and effective interactions.
Contribution
The paper develops a novel reduced Google matrix $G_R$ framework, inspired by quantum physics, to analyze subset interactions within large directed networks.
Findings
$G_R$ captures effective interactions among subset nodes.
Method allows analysis of indirect links in large networks.
Provides numerical methods for computing $G_R$.
Abstract
Using parallels with the quantum scattering theory, developed for processes in nuclear and mesoscopic physics and quantum chaos, we construct a reduced Google matrix which describes the properties and interactions of a certain subset of selected nodes belonging to a much larger directed network. The matrix takes into account effective interactions between subset nodes by all their indirect links via the whole network. We argue that this approach gives new possibilities to analyze effective interactions in a group of nodes embedded in a large directed networks. Possible efficient numerical methods for the practical computation of are also described.
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum chaos and dynamical systems · Cold Atom Physics and Bose-Einstein Condensates
