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 Mat. Zametki, 2006, Volume 80, Issue 6, Pages 908–919 (Mi mz3366)

On a matrix-based measure of the degree of coreness of a node in a network

V. M. Chelnokov, V. L. Zefirova

"Integral" Research Institute

Abstract: The paper focuses on the right and left eigenvectors of a network matrix that belong to the largest eigenvalue. It is shown that each of vector entries measures the walk centrality of the corresponding node's position in the network's link structure and of the positions of the node's adjacent nodes; as a result, it indicates to which degree the node can be associated with the structure's core, i.e., the structural coreness of the node. The relationship between the vectors' coordinates and the position of the nodes, as well as the actual computation of the coordinates, is based on an iterative computational scheme known as the power method. The paper studies the method's convergence for networks of different structure. Some possible applications are discussed. The paper also includes a numerical example dealing with a real network of $197$ nodes and $780$ links.

DOI: https://doi.org/10.4213/mzm3366

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English version:
Mathematical Notes, 2006, 80:6, 853–862

Bibliographic databases:

UDC: 519.17
Revised: 10.02.2006

Citation: V. M. Chelnokov, V. L. Zefirova, “On a matrix-based measure of the degree of coreness of a node in a network”, Mat. Zametki, 80:6 (2006), 908–919; Math. Notes, 80:6 (2006), 853–862

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz3366
• https://doi.org/10.4213/mzm3366
• http://mi.mathnet.ru/eng/mz/v80/i6/p908

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This publication is cited in the following articles:
1. V. M. Chelnokov, V. L. Zefirova, “A Matrix-Based Measure of Inter-Node Walk Relatedness in a Network”, Math. Notes, 85:1 (2009), 109–119
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