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Is the Urban World Small? The Evidence for Small World Structure in Urban Networks

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Abstract

The initial definition of small world networks triggered a rush among network scientists, working in a variety of fields and with data from many different contexts, to identify and document empirical examples of small world networks. Researchers studying urban networks – networks of cities and networks in cities – have also participated in this exercise, but because their work took place in a variety of disciplines, no definitive answer has emerged to the question: Is the urban world small? I answer this question through a systematic review of the evidence for small world structure in 172 urban networks. I find that although authors often claim urban networks are small world (71.5%), such claims are rarely grounded in a formal index or guided by a specific decision rule, and may overestimate the ubiquity of this structure. However, existing indices of small worldliness offer promising options for summarizing the extent to which an urban network is small world. I conclude with recommendations that urban network researchers make use of these indices and begin conceptualizing small worldliness as a continuous, rather than binary, characteristic.

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Notes

  1. It is important to observe that the clustering coefficient can be computed either as a global metric based on the number of closed triplets, or as the mean of a local clustering coefficient based on whether a node’s neighbors are connected to each other. Frequently authors did not report which approach was used to compute the reported clustering coefficient. The Watts-Strogatz definition of small worldliness is grounded in the mean-local metric, and for the sake of analysis below, it is assumed this is what is reported by authors.

  2. The following papers are not cited elsewhere but were included in the review: Ansell et al. 2016; Brown et al. 2013; Chatterjee 2015; Chatterjee et al. 2016; Duan and Lu 2013, 2015; Ducruet and Notteboom 2012; Gao et al. 2007; Herrera-Yagüe et al. 2015; Ibanez 2015; Iovanovici et al. 2014; Jiang 2003; Johansson 2007; Kaltenbrunner et al. 2013; Liu 2007; Liu and Xiong 2016; Luo et al. 2016; Ma et al. 2011; Maniadakis and Varoutas 2012; Mansilla and Mendozas 2010; Mukherjee 2012; Porta et al. 2006; Saberi et al. 2017; Shi and Lu 2007; Sun 2013; Thakur 2012; Wang et al. 2014a, b; Xu et al. 2007; Yazdani and Jeffrey 2011; Zhang and Li 2012; Zhang et al. 2012.

  3. As expected, none of the planar networks in this sample were identified as having a small world structure. In principle, small worldliness could be investigated in planar networks by comparing their C and L values to those in reference planar random and lattice networks, however these values are not easy to compute.

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  1. Department of Psychology, Michigan State University, East Lansing, MI, 48824, USA

    Zachary Neal

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Neal, Z. Is the Urban World Small? The Evidence for Small World Structure in Urban Networks. Netw Spat Econ 18, 615–631 (2018). https://doi.org/10.1007/s11067-018-9417-y

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