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Principal eigenvector localization and centrality in networks: Revisited

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  • Pradhan, Priodyuti
  • C.U., Angeliya
  • Jalan, Sarika

Abstract

Complex networks or graphs provide a powerful framework to understand importance of individuals and their interactions in real-world complex systems. Several graph theoretical measures have been introduced to access importance of the individual in systems represented by networks. Particularly, eigenvector centrality (EC) measure has been very popular due to its ability in measuring importance of the nodes based on not only number of interactions they acquire but also particular structural positions they have in the networks. Furthermore, the presence of certain structural features, such as the existence of high degree nodes in a network is recognized to induce localization transition of the principal eigenvector (PEV) of the network’s adjacency matrix. Localization of PEV has been shown to cause difficulties in assigning centrality weights to the nodes based on the EC. We revisit PEV localization and its relation with failure of EC problem, and by using simple model networks demonstrate that in addition to the localization of the PEV, the delocalization of PEV may also create difficulties for using EC as a measure to rank the nodes. Our investigation while providing fundamental insight to the relation between PEV localization and centrality of nodes in networks, suggests that for the networks having delocalized PEVs, it is better to use degree centrality measure to rank the nodes.

Suggested Citation

  • Pradhan, Priodyuti & C.U., Angeliya & Jalan, Sarika, 2020. "Principal eigenvector localization and centrality in networks: Revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    • Handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437120300200
    DOI: 10.1016/j.physa.2020.124169
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Parand, Fereshteh-Azadi & Rahimi, Hossein & Gorzin, Mohsen, 2016. "Combining fuzzy logic and eigenvector centrality measure in social network analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 24-31.
    3. Gabriele Lohmann & Daniel S Margulies & Annette Horstmann & Burkhard Pleger & Joeran Lepsien & Dirk Goldhahn & Haiko Schloegl & Michael Stumvoll & Arno Villringer & Robert Turner, 2010. "Eigenvector Centrality Mapping for Analyzing Connectivity Patterns in fMRI Data of the Human Brain," PLOS ONE, Public Library of Science, vol. 5(4), pages 1-8, April.
    4. Yin, Ran-Ran & Guo, Qiang & Yang, Jian-Nan & Liu, Jian-Guo, 2018. "Inter-layer similarity-based eigenvector centrality measures for temporal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 165-173.
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    Cited by:

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    3. Khanra, Pitambar & Ghosh, Subrata & Alfaro-Bittner, Karin & Kundu, Prosenjit & Boccaletti, Stefano & Hens, Chittaranjan & Pal, Pinaki, 2022. "Identifying symmetries and predicting cluster synchronization in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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