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Line graphs of weighted networks for overlapping communities

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  • T. S. Evans
  • R. Lambiotte

Abstract

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an alternative, valuable representation of the system’s topology, and are shown to have important applications in community detection, as the usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities. We apply it to the analysis of different social and geographical networks. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Suggested Citation

  • T. S. Evans & R. Lambiotte, 2010. "Line graphs of weighted networks for overlapping communities," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 77(2), pages 265-272, September.
    • Handle: RePEc:spr:eurphb:v:77:y:2010:i:2:p:265-272
    DOI: 10.1140/epjb/e2010-00261-8
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    Cited by:

    1. Zhou, Xu & Liu, Yanheng & Wang, Jian & Li, Chun, 2017. "A density based link clustering algorithm for overlapping community detection in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 65-78.
    2. Badie, Reza & Aleahmad, Abolfazl & Asadpour, Masoud & Rahgozar, Maseud, 2013. "An efficient agent-based algorithm for overlapping community detection using nodes’ closeness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5231-5247.
    3. Contreras-Aso, Gonzalo & Criado, Regino & Vera de Salas, Guillermo & Yang, Jinling, 2023. "Detecting communities in higher-order networks by using their derivative graphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. T. S. Evans & N. Hopkins & B. S. Kaube, 2012. "Universality of performance indicators based on citation and reference counts," Scientometrics, Springer;Akadémiai Kiadó, vol. 93(2), pages 473-495, November.
    5. Goetz, Stephan J. & Han, Yicheol, 2015. "Identifying Labor Market Areas Based on Link Communities," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 204870, Agricultural and Applied Economics Association.
    6. Criado-Alonso, Ángeles & Aleja, David & Romance, Miguel & Criado, Regino, 2022. "Derivative of a hypergraph as a tool for linguistic pattern analysis," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    7. Zhou, Xu & Liu, Yanheng & Zhang, Jindong & Liu, Tuming & Zhang, Di, 2015. "An ant colony based algorithm for overlapping community detection in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 289-301.
    8. Alexander Ponomarenko & Leonidas Pitsoulis & Marat Shamshetdinov, 2021. "Overlapping community detection in networks based on link partitioning and partitioning around medoids," PLOS ONE, Public Library of Science, vol. 16(8), pages 1-43, August.
    9. Iglesias Pérez, Sergio & Moral-Rubio, Santiago & Criado, Regino, 2021. "A new approach to combine multiplex networks and time series attributes: Building intrusion detection systems (IDS) in cybersecurity," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Kire Trivodaliev & Aleksandra Bogojeska & Ljupco Kocarev, 2014. "Exploring Function Prediction in Protein Interaction Networks via Clustering Methods," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-16, June.
    11. Criado-Alonso, Ángeles & Battaner-Moro, Elena & Aleja, David & Romance, Miguel & Criado, Regino, 2021. "Enriched line graph: A new structure for searching language collocations," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    12. Zhenping Li & Xiang-Sun Zhang & Rui-Sheng Wang & Hongwei Liu & Shihua Zhang, 2013. "Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-10, December.
    13. Dongxiao He & Di Jin & Carlos Baquero & Dayou Liu, 2014. "Link Community Detection Using Generative Model and Nonnegative Matrix Factorization," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-10, January.
    14. Johannes Wachs & Mih'aly Fazekas & J'anos Kert'esz, 2019. "Corruption Risk in Contracting Markets: A Network Science Perspective," Papers 1909.08664, arXiv.org.

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