Spatial associations in global household bicycle ownership


The interest in bicycling and its determining factors is growing within the public health, transportation and geography communities. Ownership is one factor affecting bicycle usage, but work is still ongoing to not only quantify its effects but also to understand patterns in its growth and influence. In recent work, we mined and discovered patterns in global bicycle ownership that showed the existence of four characteristic country groups and their trends. Building on these results, we show in this paper that the ownership dataset can be modeled as a network. First, we observe mixing tendencies that indicate neighboring countries are more likely to be in the same ownership group and we map the likelihoods for cross-group mixings. Further, we define the strength of connections between countries by their proximity in ownership levels. We then determine the weighted degree assortative coefficient for the network and for each group relative to the network. We find that while the weighted degree assortativity of the ownership network is statistically insignificant, the highest and lowest ownership groups exhibit disassortative behavior with respect to the entire network. The second and third ranked groups, however, are strongly assortative. Our model serves as a step toward further work in studying the relationship between proximity and bicycle ownership among nations and unearthing possible patterns of influence. Considering further developments, this work can inform policy-relevant recommendations toward regional planning. This effort also contributes to expanding research in assortativity analyses, especially in weighted networks.

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  1. 1.

    The data and supporting code are available at

  2. 2.

    The dynamic time warping algorithm was first introduced by Bellman and Kalaba (1959). Its application was subsequently furthered by Sakoe and Chiba (1978). See Giorgino (2009) for more on its execution in R.

  3. 3.

    The error term is given by \(\varepsilon _{k} = \sqrt{\left(1 + \frac{1}{B}\right)\frac{1}{B} \sum _{b}\left\rbrace \log (W_{k,b}^{*}) - \frac{1}{B}\sum _{b}\log (W^{*}_{k,b})\right\lbrace ^{2}}\), where b is the index number of the generated sample (Tibshirani et al. 2001).

  4. 4.

    For a complete discussion on the global and group trends, please refer to Oke et al. (2015). Also, trends in bicycle ownership for each country in the dataset set can be viewed in Appendix B (Ibid).

  5. 5.

    Subsequent summations over i or j are over the same ranges indicated in Eq. 3.2.

  6. 6.

    This threshold corresponds to the Z-score, for which \(3\sigma \) or \(2\sigma \) are commonly employed as the minimum value for significance. Here, we use the more stringent \(5\sigma \) threshold (Colquhoun 2014; Foster et al. 2010; Newman 2002).

  7. 7.

    Subsequent summations over b or c are on the same set D, except where otherwise noted.


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We thank the participants of the 2014 INFORMS Workshop on Data Mining and Analytics participants for their valuable comments in the earlier stages of our work. The Gordon Croft Fellowship awarded by the Energy, Environment, Sustainability and Health Institute \((\hbox {E}^{2}\hbox {SHI})\) at The Johns Hopkins University, Baltimore, Maryland, funded this research in part. This quality of this paper was greatly improved as a result of the work of the two anonymous reviewers to whom the authors are grateful.

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Correspondence to Olufolajimi Oke.

Appendix: Country parameters

Appendix: Country parameters

Table 6 lists the degree parameters for each country. The code (written in Python) and supporting data for this work are available at

Table 6 Degree, weighted degree, average neighbor weighted degree and group membership of the countries in the dataset

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Oke, O., Bhalla, K., Love, D.C. et al. Spatial associations in global household bicycle ownership. Ann Oper Res 263, 529–549 (2018).

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  • Bicycle ownership
  • Spatial associations
  • Networks
  • Assortativity