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Rich-club ordering and the dyadic effect: Two interrelated phenomena

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  • Cinelli, Matteo
  • Ferraro, Giovanna
  • Iovanella, Antonio

Abstract

Rich-club ordering and the dyadic effect are two phenomena observed in complex networks that are based on the presence of certain substructures composed of specific nodes. Rich-club ordering represents the tendency of highly connected and important elements to form tight communities with other central elements. The dyadic effect denotes the tendency of nodes that share a common property to be much more interconnected than expected. In this study, we consider the interrelation between these two phenomena, which until now have always been studied separately. We contribute with a new formulation of the rich-club measures in terms of the dyadic effect. Moreover, we introduce certain measures related to the analysis of the dyadic effect, which are useful in that they confirm the presence and relevance of rich-clubs in complex networks and provide certain insights and a baseline for the evaluation of the rich-club size. In addition, certain computational experiences show the usefulness of the introduced quantities with regard to different classes of real networks.

Suggested Citation

  • Cinelli, Matteo & Ferraro, Giovanna & Iovanella, Antonio, 2018. "Rich-club ordering and the dyadic effect: Two interrelated phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 808-818.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:808-818
    DOI: 10.1016/j.physa.2017.08.122
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    References listed on IDEAS

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    1. Giovanna Ferraro & Antonio Iovanella & Gianluca Pratesi, 2016. "On the influence of nodes' characteristic in inter-organisational innovation networks structure," International Journal of Computational Economics and Econometrics, Inderscience Enterprises Ltd, vol. 6(3), pages 239-257.
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    Cited by:

    1. Matteo Cinelli & Valerio Ficcadenti & Jessica Riccioni, 2021. "The interconnectedness of the economic content in the speeches of the US Presidents," Annals of Operations Research, Springer, vol. 299(1), pages 593-615, April.
    2. Sebastian Ion Ceptureanu & Eduard Gabriel Ceptureanu & Cristian Eugen Luchian & Iuliana Luchian, 2018. "Community Based Programs Sustainability. A Multidimensional Analysis of Sustainability Factors," Sustainability, MDPI, vol. 10(3), pages 1-15, March.
    3. Zhang, Yifan & Ng, S. Thomas, 2021. "Unveiling the rich-club phenomenon in urban mobility networks through the spatiotemporal characteristics of passenger flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    4. Roy Cerqueti & Giulia Rotundo & Marcel Ausloos, 2021. "Tsallis entropy for cross-shareholding network configurations," Papers 2109.04214, arXiv.org.
    5. Abreu, Mariana Piaia & Grassi, Rosanna & Del-Vecchio, Renata R., 2019. "Structure of control in financial networks: An application to the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 302-314.
    6. Matteo Cinelli & Valerio Ficcadenti & Jessica Riccioni, 2020. "The interconnectedness of the economic content in the speeches of the US Presidents," Papers 2002.07880, arXiv.org.
    7. Matteo Cinelli & Giovanna Ferraro & Antonio Iovanella & Giulia Rotundo, 2021. "Assessing the impact of incomplete information on the resilience of financial networks," Annals of Operations Research, Springer, vol. 299(1), pages 721-745, April.
    8. Matteo Cinelli & Giovanna Ferraro & Antonio Iovanella, 2017. "Resilience of Core-Periphery Networks in the Case of Rich-Club," Complexity, Hindawi, vol. 2017, pages 1-12, December.
    9. Cerqueti, Roy & Clemente, Gian Paolo & Grassi, Rosanna, 2021. "Stratified cohesiveness in complex business networks," Journal of Business Research, Elsevier, vol. 129(C), pages 515-526.

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