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Statistical Analysis of Weighted Networks

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  • I. E. Antoniou
  • E. T. Tsompa

Abstract

The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.

Suggested Citation

  • I. E. Antoniou & E. T. Tsompa, 2008. "Statistical Analysis of Weighted Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-16, May.
    • Handle: RePEc:hin:jnddns:375452
    DOI: 10.1155/2008/375452
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    Cited by:

    1. Clemente, G.P. & Grassi, R., 2018. "Directed clustering in weighted networks: A new perspective," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 26-38.
    2. Guo, Lei & Guo, Minxin & Wu, Youxi & Xu, Guizhi, 2023. "Specific neural coding of fMRI spiking neural network based on time coding," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Rosati, Nicoletta & Bomprezzi, Pietro & Martinez Cillero, Maria, 2024. "Critical dimensions in the empirical measurement of common shareholding," Research in International Business and Finance, Elsevier, vol. 70(PA).
    4. Guo, Lei & Liu, Chengjun & Wu, Youxi & Xu, Guizhi, 2023. "fMRI-based spiking neural network verified by anti-damage capabilities under random attacks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. Li, Jie & Wang, Lidan & Zhou, Zhong-Qiang & Zhang, Yongjie, 2021. "Monitoring or tunneling? Information interaction among large shareholders and the crash risk of the stock price," Pacific-Basin Finance Journal, Elsevier, vol. 65(C).
    6. Ahmadi, Negar & Pei, Yulong & Pechenizkiy, Mykola, 2019. "Effect of linear mixing in EEG on synchronization and complex network measures studied using the Kuramoto model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 289-308.
    7. Schuster, Hannah & Polleres, Axel & Wachs, Johannes, 2024. "Stress-testing road networks and access to medical care," Transportation Research Part A: Policy and Practice, Elsevier, vol. 181(C).

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