RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 1 scientific paper (total in 1 paper)

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

Full text: PDF file (537 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.17
Received: 14.09.2005
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
\Bibitem{CheZef06}
\by V.~M.~Chelnokov, V.~L.~Zefirova
\paper On a matrix-based measure of the degree of coreness of a node in a network
\jour Mat. Zametki
\yr 2006
\vol 80
\issue 6
\pages 908--919
\mathnet{http://mi.mathnet.ru/mz3366}
\crossref{https://doi.org/10.4213/mzm3366}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2311617}
\zmath{https://zbmath.org/?q=an:1130.68018}
\elib{http://elibrary.ru/item.asp?id=9429653}
\transl
\jour Math. Notes
\yr 2006
\vol 80
\issue 6
\pages 853--862
\crossref{https://doi.org/10.1007/s11006-006-0207-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243368900026}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845618686}


Linking options:
  • http://mi.mathnet.ru/eng/mz3366
  • https://doi.org/10.4213/mzm3366
  • http://mi.mathnet.ru/eng/mz/v80/i6/p908

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:340
    Full text:90
    References:24
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020