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Correlation between centrality metrics and their application to the opinion model

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  • Cong Li
  • Qian Li
  • Piet Mieghem
  • H. Stanley
  • Huijuan Wang

Abstract

In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The mth-order degree mass of a node is the sum of the weighted degree of the node and its neighbors no further than m hops away. We find that the betweenness, the closeness, and the components of the principal eigenvector of the adjacency matrix are strongly correlated with the degree, the 1st-order degree mass and the 2nd-order degree mass, respectively, in both network models and real-world networks. We then theoretically prove that the Pearson correlation coefficient between the principal eigenvector and the 2nd-order degree mass is larger than that between the principal eigenvector and a lower order degree mass. Finally, we investigate the effect of the inflexible contrarians selected based on different centrality metrics in helping one opinion to compete with another in the inflexible contrarian opinion (ICO) model. Interestingly, we find that selecting the inflexible contrarians based on the leverage, the betweenness, or the degree is more effective in opinion-competition than using other centrality metrics in all types of networks. This observation is supported by our previous observations, i.e., that there is a strong linear correlation between the degree and the betweenness, as well as a high centrality similarity between the leverage and the degree. Copyright The Author(s) 2015

Suggested Citation

  • Cong Li & Qian Li & Piet Mieghem & H. Stanley & Huijuan Wang, 2015. "Correlation between centrality metrics and their application to the opinion model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(3), pages 1-13, March.
  • Handle: RePEc:spr:eurphb:v:88:y:2015:i:3:p:1-13:10.1140/epjb/e2015-50671-y
    DOI: 10.1140/epjb/e2015-50671-y
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    Cited by:

    1. Manuel, Paul & Brešar, Boštjan & Klavžar, Sandi, 2022. "The geodesic-transversal problem," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Li, Jin-Yue & Li, Xiang & Li, Cong, 2021. "The Kronecker-clique model for higher-order clustering coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    3. Stephany Rajeh & Marinette Savonnet & Eric Leclercq & Hocine Cherifi, 2023. "Comparative evaluation of community-aware centrality measures," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(2), pages 1273-1302, April.
    4. Gobbo, Simone Cristina de Oliveira & Mariano, Enzo Barberio & Gobbo Jr., José Alcides, 2021. "Combining social network and data envelopment analysis: A proposal for a Selection Employment Contracts Effectiveness index in healthcare network applications," Omega, Elsevier, vol. 103(C).
    5. Abreu, Mariana Piaia & Del-Vecchio, Renata R. & Grassi, Rosanna, 2020. "Analysis of productive structure applying network theory: The Brazilian case," Structural Change and Economic Dynamics, Elsevier, vol. 53(C), pages 281-291.
    6. Natarajan Meghanathan, 2019. "Unit Disk Graph-Based Node Similarity Index for Complex Network Analysis," Complexity, Hindawi, vol. 2019, pages 1-22, March.

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    Statistical and Nonlinear Physics;

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