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.