Did Zipf Anticipate Spatial Connectivity Structures?

Abstract

An avalanche of empirical studies has addressed the validity of the rank-size rule (or Zipf's law) in a multicity context in many countries. Under which conditions (eg, sample size, spatial scale) this ‘law’ holds remains as yet largely underinvestigated, while spatial network constellations also deserve more attention. Against this background, we investigate the relationship between network connectivity and the rank-size rule (or Zipf's law) in an urban economic network constellation. In particular, we address the following methodological issues: (i) the (aggregate) behavioural foundation underlying the rank-size rule (Zipf's law) in the light of spatial-economic network theories (eg, entropy maximization, spatial interaction theory); (ii) the nature of the analytical relationship between social-spatial network analysis and the rank-size rule (Zipf's law). We argue that the rank-size rule is compatible with conventional economic foundations of spatial network models. We test the sensitivity of rank-size rules for changes in scale, functional forms, time periods, and connectivity structures. Our application uses an extensive spatiotemporal panel database on the evolution of the urban population in Germany. We test the relevance of the rank-size rule (Zipf's law), and—in parallel—the related ‘socioeconomic’ connectivity in these urban networks. In particular, we will show that Zipf's law (ie, with the rank-size coefficient equal to 1) is only valid under particular conditions of the sample size.

Geography in motion: Hexagonal spatial systems in fuzzy gravitation

“…A gravitational attractor is an area of attraction of trajectories whose source is the force of gravity. The theory of geographical potential is an important component of socio-economic geography (Janowski, 1908/2013; Nijkamp and Reggiani, 1988; Pumain, 1982; Reggiani and Nijkamp, 2014; Stewart, 1948; Wilson, 2009). In a previous study (Banaszak et al., 2015), the authors have demonstrated that hierarchically organized spatial systems (or CPT-like systems) display in a dynamic context a fractal structure of spatial interactions (for example, in case of cities).…”

“…There is an avalanche of literature on the statistical-econometric mapping and testing of hierarchical regularities among spatial actors or units in a complex spatial urban or regional and industrial world (see e.g. Batty, 2013; Reggiani and Nijkamp, 2014). Thus far, much less attention has been given to the underlying complex dynamics in shaping such rank-size or hierarchical patterns.…”

Pareto or Log‐normal? Best Fit and Truncation in the Distribution of All Cities*

“…Mori, Nishikimi, and Smith () propose a link between industries spatial intensity and population intensity. Finally, Reggiani and Nijkamp () interpret the estimated coefficient as an indicator of economic development in terms of the urban structure, intended as a socioeconomic connected network…”

Cautionary Notes on the Rank‐size Distribution

“…That said, recent work by Mori et al . () points to various possibilities for incorporating spatial elements into the rank‐size distribution, as does the study by Reggiani and Nijkamp ().…”