How sensitive are measures of polycentricity to the choice of ‘centres’? A methodological and empirical exploration

Abstract

Chinese

In the literature dealing with measuring ‘urban polycentricity’, relatively little attention has been paid to the identification of what constitutes an ‘urban centre’. In this paper, we assess the sensitivity of polycentricity measures to one particular aspect of this identification: using the case of ‘polycentric urban regions’, we empirically examine the sensitivity of the ‘level’ of polycentricity to the number of cities included in the analysis. Using a two-mode firm–city data source, we do so by stepwise measuring the polycentricity of the Yangtze River Delta (YRD) as cities are added to the analysis. This measurement of ‘stepwise polycentricity’ is benchmarked against an ideal typical urban system with a rank-size distribution. The results suggest that the measure of polycentricity is indeed highly sensitive to the choice of the number of cities, so that the alleged level of polycentricity is contingent on the choice of a cut-off point. We propose that the analysis of the sensitivity of polycentricity can help researchers to (1) investigate the different role of cities in shaping polycentric structures of urban regions, and (2) better identify mono- or polycentric structures of urban regions. Analyses of trends in the ‘stepwise polycentricity’ of the YRD and seven other urban regions along the Yangtze River Economic Belt serve to illustrate.

Keywords

China polycentricity rank-size sensitivity analysis urban regions Yangtze River Delta

Introduction

‘Polycentric development’ has become a widely used term in urban research and urban policy narratives alike, as well as a normative spatial planning objective. This has been especially the case since the ‘European Spatial Development Perspective’ (European Commission, 1999) was published, where polycentric development was set as one of three main guiding principles for European spatial development. The academic debate on polycentricity now spans multiple scales (intra-urban, inter-urban or regional, national; see Hall and Pain, 2006; McDonald and McMillen, 1990; Waterhout et al., 2005), adopts different perspectives (morphological versus functional polycentricity; see Burger and Meijers, 2012) and has branched off in several sub-literatures (e.g. theoretical explorations, empirical analyses and assessments of its alleged social economic and environmental effects; see Brezzi and Veneri, 2015; Hoyler et al., 2008; Meijers and Burger, 2010). In spite of its increasing popularity, research on urban polycentricity is nonetheless characterised by a number of seemingly perennial debates. For example, its theoretical rationale has been deemed elusive (Kloosterman and Musterd, 2001; Lambregts, 2009); there is no consensus about some basic definitions (Parr, 2004); results of empirical analyses strongly vary by measurement scheme (Green, 2007; Meijers, 2008); and possible economic implications have often been asserted without substantial evidence (Davoudi, 2003; Parr, 2004; see, however, Meijers and Burger, 2010). Taken together, these debates make clear that conceptual and methodological clarity is of the utmost importance if the concept is to have analytical purchase.

To help in facilitating this clarity, we focus on a specific element of the recurring methodological conundrums when measuring ‘urban polycentricity’: the question of what constitutes a ‘centre’. Although the conceptual and operational definition of a ‘centre’ is of paramount importance in any measurement exercise, its impact has not always been recognised. The issue of a proper definition and identification of a ‘centre’ itself has many aspects, ranging from the territorial/scalar outline of centres (e.g. legal cities, municipal administrative areas or urban agglomerations; cf. Burger et al., 2008) to the question of how many centres should be included when formally assessing polycentricity (Meijers, 2008). The literature on the former issues has focused on investigating the remit of the modifiable areal unit problem in identifying agglomeration externalities (Burger et al., 2008) and examining the size distribution of cities (Rosen and Resnick, 1979). These analyses consistently show that the identification of polycentricity and its effects is indeed dependent on the scales of analysis (e.g. Amrhein, 1995; Dewhurst and McCann, 2007). Much less research has been devoted to the number of centres to be included, that is, the cut-off point used to single out which centres should be included in the analysis of polycentricity. An important exception is the work of Meijers (2008), who argued that the choice of the threshold for inclusion of cities will affect polycentricity measures. This, in turn, echoes Schaffar and Dimou’s (2012) broader observation that the assumption of the presence of a rank-size distribution in an urban hierarchy is questionable when taking into account all cities rather than only the ‘main cities’. In this paper, we contribute to this line of research by specifically focusing on this issue in the context of ‘polycentric urban regions’ (PURs).

PURs are generally defined as urbanised regions having a ‘relative balance’ between a set of important ‘urban centres’ within the region (Burger and Meijers, 2012; Green, 2007; Kloosterman and Musterd, 2001; Lambregts, 2009; Parr, 2004; Vasanen, 2013). This does not necessarily mean that all cities within the region need to have a ‘similar’ size, as a PUR not only consists of a series of inter-connected large cities but also a range of medium-sized and smaller centres. When assessing the level of polycentricity in a putative PUR, without clear rationale on which and how many cities to include, the results of a measurement exercise may be shaped by the pre-hoc selection of centres. In other words, the level of polycentricity may be contingent upon the choice of the number of centres and, in this paper, we seek to reveal some of the major contours of this sensitivity.

As suggested, the issue of identifying which settlements to include has been raised by Meijers (2008), who proposed that a fixed number of cities could be adopted when assessing different PURs. Although most scholars acknowledge that the identification of settlements is an important step before engaging in analyses (e.g. Green, 2007; Hall and Pain, 2006), the issue of the actual sensitivity of polycentricity to the choice of cities has not received specific attention in the literature. One possible reason is that PUR debates – which have mostly been articulated in (north-western) Europe – are often linked to a series of small- and medium-sized cities of roughly equal importance (see Dijkstra et al., 2013). In this case, the effect of the choice of cities on measures of polycentricity may seem to be of secondary importance. For instance, according to Meijers and Sandberg (2008) in their measurement of the polycentricity of Germany, Sweden and Greece, results when selecting the top ten cities correlate strongly with results for the top five or 20 cities. However, this does not imply that this is a minor issue per se. Evidence can be found in the ESPON (European Spatial Planning Observation Network) measures of the polycentricity of EU countries (ESPON Monitoring Committee, 2006), which seems to produce inconsistent results regarding ‘the tentative impressions of the extent of polycentricity of (measured) countries’ because many smaller centres are included (cf. Meijers, 2008). Moreover, there is a growing tendency to apply the concept of PURs in understanding urban regions in which there is a ‘large city logic’, including urban regions in China (e.g. Li and Phelps, 2016, 2018; Liu et al., 2018; Song, 2014) and Latin America (Fernández-Maldonado et al., 2014). In these regions there is often a major gap between large cities and small cities in terms of their ‘importance’ (however measured). As Li and Phelps (2018: 12) have noticed in the case study of the Yangtze River Delta (YRD), the degree of polycentricity (of the YRD) decreases as the sample size increases. In other words: in such cases, adding many small cities into the measurement of polycentricity may strongly influence the ‘balance’ among the cities included in the analysis. As a result, explicitly investigating how sensitive the ‘level’ of polycentricity is to the number of cities included in analyses can be assumed to be important in measurement schemes.

Against this backdrop, the main objective of this paper is to explore the sensitivity of polycentricity in PURs to the choice of the number cities. In practice, we do this by stepwise measuring the polycentricity of a putative PUR as cities are added. The evolution of this ‘stepwise polycentricity’ (SP) may provide direct evidence of the sensitivity of polycentricity to the choice of cities. However, sensitivity is much more than a matter of absolute change of the level of polycentricity, as how to define ‘sensitivity’ is a complex issue in itself: how sensitive measures are depends on the number of cities in and of themselves (e.g., a regional system with 15 cities may be less prone than one consisting of five cities), so that we need a transparent yardstick that is independent of the number of cities. To this end, we develop a methodology benchmarking our measure of sensitivity. This benchmarking procedure uses an abstract urban system with a rank-size hierarchical distribution, which can be envisaged as representing a middle ground between ideal typical monocentric and polycentric regions (Berry and Okulicz-Kozaryn, 2012; Rosen and Resnick, 1979; Van Nuffel et al., 2010): only in cases where the SP of a certain region exhibits exceptional change compared with a benchmark region with the same number of cities, can this region be deemed to be sensitive to the choice of cities. Furthermore, as the SP measurement quantifies the ‘balance’ among all the possible combinations of urban centres, the change of SP has the potential to uncover the roles each city plays in shaping a PUR. In addition, different structures of urban regions are assumed to exhibit different patterns of SP change. Varied patterns of SP change, in turn, have the potential to identify mono- or polycentric structures of urban regions. Taken together, a second objective of this paper is thus to explore what we can ‘gain’ from an investigation of SP.

Our research uses the YRD, an archetypal mega-city region in China, as the empirical setting. Based on a bipartite network projection (Liu and Derudder, 2012) of a data source detailing firm–city interactions, we (re-)examine the polycentric structure of the YRD by applying SP measurements. Furthermore, to show the wider significance of our measure of SP for identifying different mono- or polycentric structures of urban regions, we chart the SP of seven further urban regions along the Yangtze River Economic Belt (YREB). The remainder of this paper is organised as follows. The next section presents our approach to measuring SP, introduces the case study regions and describes our data. We then discuss the results of the empirical analysis, which is developed in three parts: we show and discuss the benchmarked SP of the YRD, investigate the role of different cities of the YRD in shaping its polycentric structure, and present a comparative analysis among other urban regions along the YREB. This is followed by an overview of the major conclusions that can be drawn from our analysis.

Methods, case study regions and data

Methods: Measuring stepwise polycentricity (SP)

We propose a stepwise procedure to assess how measures of polycentricity respond to the change of the number of cities that are added to analyses. This procedure consists of three simple steps: first, ranking the importance of cities; second, stepwise measuring the polycentricity among the top n cities; and third, benchmarking the changes of SPs by employing an ideal typical urban system with a rank-size distribution as per Zipf. In operational terms, we can apply any of the existing methods in the literature of quantifying polycentricity to rank the importance of cities and measure their balance.

Ranking the size of cities

In the literature on quantifying polycentricity, the size of cities can be defined by means of (1) a morphological perspective, which is based on attribute features such as GDP and population size (Burgalassi, 2010; ESPON Monitoring Committee, 2007); and (2) a functional perspective, which is based on the structure of linkages such as incoming and/or outgoing communication flows (Burgalassi, 2010; De Goei et al., 2010). Morphological measures and functional measures are, however, not incommensurable. Burger and Meijers (2012) propose a theoretical framework linking both approaches (see also the application in Liu et al., 2016). Put simply, a city’s morphological importance consists of three components: a within-system component based on intra-regional flows, an outside-system component based on regions’ external flows, and a local component based on intra-city flows. Given this paper’s focus on PURs, cities’ local flows are deemed to be of lesser importance, and we therefore only consider intra-regional and external flows of regions. As a result, a city’s total volume of functional connections with all other cities within and outside the regional system in which it is located (i.e. total centrality) provide the basis for measuring morphological polycentricity. Meanwhile, using the same analytical framework, a city’s functional importance is only related to its functional connections within the regional urban system (i.e. regional centrality) (for more details, see Burger and Meijers, 2012).

As urban polycentricity is often analysed from both morphological and functional perspectives (e.g. Burger and Meijers, 2012; Green, 2007; Hall and Pain, 2006), to strengthen the comprehensiveness of the empirical investigation in this paper, we will assess the sensitivity of both morphological polycentricity and functional polycentricity.

Measuring ‘balance’ in city-size distributions

Various methodologies have been developed for quantifying the ‘balance’ in city-size distributions, such as measuring the rank-size distribution of cities’ size (Burgalassi, 2010; ESPON Monitoring Committee, 2006; Parr, 2004), evaluating the variance of cities’ size (Hanssens et al., 2014), and benchmarking the distribution of cities’ size through a comparison with some dummy or ideal-typical mono- or polycentric distributions (Green, 2007; Hanssens et al., 2014) (for a detailed review, see Liu et al., 2016).

In this paper, we adopt the method originally developed by Green (2007) and subsequently extended by Liu et al. (2016) to stepwise measure morphological and functional polycentricity. Green’s method standardises polycentric indicators through a comparison with a completely monocentric two-node network. Morphological polycentricity is calculated as:

P_{M} (n) = 1 - σ_{m} / σ_{mmax}

(1)

where: $P_{M} (n)$ is the morphological polycentricity of an urban region by taking into account the top n cities, ranging from 0 (absolute monocentricity) to 1 (absolute polycentricity); $σ_{m}$ is the standard deviation of cities’ total centrality; $σ_{mmax}$ is the standard deviation of nodes’ total centrality of a two-node network where one node’s total centrality equals 0, and the other’s total centrality equals the highest total centrality in the city set N.

Functional polycentricity can be calculated as follows:

P_{F} (n) = (1 - σ_{f} / σ_{fmax}) \times Δ

(2)

where $P_{F} (n)$ is the functional polycentricity of an urban region by taking into account the top n cities, ranging from 0 (absolute monocentricity) to 1 (absolute polycentricity); $σ_{f}$ is the standard deviation of cities’ regional centrality; $σ_{fmax}$ is the standard deviation of nodes’ regional centrality of a two-node network where one node’s regional centrality equals 0 and the other’s regional centrality equals the highest regional centrality in the city set N; $Δ$ is the network density of city set N, which is defined as the ratio of the total intercity connections to the maximum of intercity connections that is theoretically possible (see also Green, 2007; Liu et al., 2016).

Benchmarking the changes in SP

Simply looking at the absolute changes of SP exposes how the measure of polycentricity changes when the number of cities changes. However, there may be a problem of possible misjudgement of the sensitivity, as the interpretation of the SP is itself contingent upon the number of nodes. Therefore, the change trend of SP needs to be verified in relation to a benchmark region, ideally a region with the same number of cities that can be used to benchmark mono- or polycentric distributions. Here, an urban system with an ideal typical rank-size distribution is employed.

The rank-size rule, which states that the nth ranked city has a centrality of 1/n of the largest city within an urban system (Zipf, 1941), has been deemed one of the most empirical regularities in the distribution of city sizes across space and time (Carroll, 1982; Fujita et al., 1999; Rosen and Resnick, 1979). The reason for employing this distribution as a benchmark is by no means normative but because it can be said to represent a mathematical middle ground between ideal typical monocentric and polycentric regions. The coefficient of its slope has been widely employed as a breakpoint to classify monocentric and polycentric regions: a region having a flatter rank-size distribution than a Zipf distribution can be deemed more polycentric, while a region having a steeper rank-size distribution than the Zipf distribution can be deemed more monocentric.

The third step, therefore, is to benchmark the change of SP by using a rank-size distribution. We do so by stepwise computing for each region the ratio between its SP and the SP of a Zipf rank-size urban system with an equal number of cities, as follows:

S P_{Benchmarked} (n) = SP (n) / S P_{Zipf} (n)

(2)

where $S P_{Benchmarked} (n)$ is the benchmarked polycentricity when taking into account the top n cities; SP(n) is the stepwise polycentricity when taking into account the top n cities, as measured by (1) and (2); and $S P_{Zipf} (n)$ is the SP of the Zipf-like urban system with an equal number of cities. The benchmarked SPs vary around 1, where values above 1 point to tendencies towards polycentricity and values less than 1 indicate tendencies towards monocentricity. In the following sections, measures of SPs refer to the benchmarked measures, unless otherwise specified.

Case study regions: YRD and seven other urban regions along the YREB

The YRD¹ comprises a series of physically separate but functionally (unevenly) interconnected cities. It consists of multiple economic, demographic and political cores: four economic centres with a GDP of over 500 billion RMB (i.e. Shanghai, Nanjing, Hangzhou and Suzhou); three demographic cores with a population of over 5 million (i.e. Shanghai, Nanjing and Hangzhou); and, politically speaking, one municipality directly under the central government (Shanghai) and three sub-provincial cities (Nanjing, Hangzhou and Ningbo). These cities are strongly interlinked through dense motorway and high-speed railway networks, which provide extensive labour markets and foster regional integration (Chen, 2012). Furthermore, the inequality in the distribution of the sizes of the cities, such as GDP and population, within the YRD is remarkable (Figure 1). The region’s putative polycentricity has repeatedly been verified in the literature (Li and Phelps, 2016, 2018; Liu et al., 2016; Song, 2014; Zhang et al., 2016). Here, we re-assess its polycentric structure using our stepwise measure.

Figure 1.

The Yangtze River Delta with its GDP and demographic distribution.

To show how the sensitivity analysis can help to identify mono- or polycentric structures of urban regions, we assess the changes in benchmarked SP in seven urban regions along the YREB. The YREB – a subnational territorial unit which covers 11 province-level administrative units with more than 40% of the national population – has been one of the two components of China’s great T-shaped territorial development strategy (the other is the coastal economic belt). This region accommodates various urban regions: apart from the YRD, other urban regions are the Wanjiang cluster, the Changsha–Zhuzhou–Xiangtan cluster, the Wuhan cluster, the Poyang Lake cluster, the Chongqing–Chengdu cluster, the Central Yunnan cluster and the Central Guizhou cluster (Figure 2). Their definitions draw upon Fang et al.’s (2010) identification, which has been acknowledged by central government agencies. The typology of these YREB urban regions varies immensely in terms of the number of cities, area and degree of polycentric development (according to Liu et al., 2016), which offers a good sample to present different mono- or polycentric patterns of urban regions.

Figure 2.

Eight urban regions along the Yangtze River Economic Belt. YRD, Yangtze River Delta; WJ, Wanjiang cluster; CZT, Changsha–Zhuzhou–Xiangtan cluster; WH, Wuhan cluster; PYL, Poyang Lake cluster; CC, Chongqing–Chengdu cluster; CYN, Central Yunnan cluster; CGZ, Central Guizhou cluster.

Data collection and processing

There is a growing literature focusing on measuring intercity connections, including through infrastructural linkages (e.g. Liu et al., 2016), proxy measures of intercity workflows through advanced service functions (e.g. Taylor and Derudder, 2016), corporate command relations (e.g. Alderson and Beckfield, 2004), knowledge collaboration (e.g. Li and Phelps, 2016, 2018) and commuting interactions (e.g. Vasanen, 2013). In our research, we employ proxy measures based upon the location strategies of business services firms. To this end, we implement the interlocking network model (INM) devised by the Globalisation and World Cities (GaWC) research group (Taylor, 2001; Taylor and Derudder, 2016) to infer intercity networks from a Chinese firm–city data set. The rationale behind the INM is that the office networks of producer services (PS) firms connect the cities in which they are located. Based on the co-presence of office networks of service firms between two cities, the connectivity of city-dyads can be calculated. Given the multiplexity of urban networks, we emphasise that this approach simply represents but one example of intercity linkages (Burger et al., 2014).

The formal specification of INM is presented in Taylor and Derudder (2016); below, we restrict ourselves to the basics of our data gathering and processing. The operationalisation of the INM starts with collecting data on the location matrix of m PS firms in n cities. In practice, this includes the selection of firms and cities and the assignment of service values (standardised measures of the importance of city to a firm).

First, the selection of firms was based on the sectoral ranking in China of eight PS sectors in 2013. A total of 247 firms were identified: 50 accountancy firms, 41 advertising firms, 23 management consultancy firms, 35 law firms, 21 bank firms, 26 insurance firms, 30 security firms and 21 trust firms.²

Second, our city list contains all 289 cities at the prefecture level and above in mainland China (China City Statistical Yearbook 2013). The end product thus is a 247 PS firms × 289 cities matrix.

The websites of these 247 PS firms provide information about the size of their presences (e.g. the number of practitioners) and their extra-locational functions (e.g. national headquarters and regional headquarters) in these 289 cities. In line with GaWC research, we encode the two types of information into standardised service values according to a six-point scale, with values ranging from 0 (no presence) to 5 (headquarters).

Based on the city-by-firm service values matrix, the city-dyad connectivity $CD C_{a - b}$ between any pair of cities a and b is defined as follows:

CD C_{a - b} = \sum_{j = 1}^{247} V_{aj} \times V_{bj}

(3)

where $V_{ij} (i = a, b)$ is the ‘service value’ of city i to firm j.

The total centrality (i.e. the index to assess morphological polycentricity) and regional centrality (i.e. the index to assess functional polycentricity) of city a are therefore computed as follows:

Total Centrality (a) = \sum_{i = 1}^{289} CD C_{a - i}

(4)

Regional Centrality (a) = \sum_{j = 1}^{m - 1} CD C_{a - j}

(5)

where i refers to all cities within and outside the urban region in which city a is located, which is limited to all 289 cities of prefecture level and above in mainland China; j refers to the cities within the same urban region in which city a is located; and m refers to the number of the cities within each of the urban regions.

Results and discussion

Stepwise polycentricity of the YRD

The result of the stepwise measurement for the YRD is shown on a scatter diagram (Figure 3). An initial observation is that the SP – in both the morphological and the functional sense – has a relatively high value when Shanghai, Nanjing and Hangzhou have been stepwise added into the analysis, after which there is a significant and gradual drop-off – particularly in functional polycentricity – when subsequent cities such as Hefei, Ningbo and Suzhou are considered. This clearly shows that the measure of polycentricity is indeed contingent on the number of cities: adopting different sample sizes will produce completely different results. The functional polycentricity based on all 26 cities, for instance, will drop from its peak value (i.e. the measurement based on the three main centres) of 2.3 to 1.6. This implies that there is a tendency towards a polycentric pattern in the YRD irrespective of the number of cities, but the intensity declines as cities are added to the analysis.

Figure 3.

Stepwise polycentricity of the YRD. NJ, Nanjing; HZ, Hangzhou; HF, Hefei; NB, Ningbo; SZ, Suzhou; WX, Wuxi; NT, Nantong; SX, Shaoxing; the tags of each point represent newly added cities.

Second, the disparity in the trend lines of morphological and functional SP is notable. This shows that the importance of the YRD’s cities as providers of regional functions is more balanced than as providers for regional and national functions combined. The larger levels of functional polycentricity can be tentatively ascribed to at least two related reasons: on the one hand, this region has been a pioneering example for implementing strategies of regional integration through intercity cooperation (Luo and Shen, 2009); on the other hand, the administrative levels of cities within the YRD are hierarchical, producing a remarkable inequality in the external influence of cities with regard to their administrative reach and economic capacity within and outside the regional urban system (Cartier, 2016).

Different roles of cities in the YRD in shaping its polycentric structure

Discussing the different role of cities of the YRD in shaping its polycentric structure is an exercise that is closely related to discussing change in SP, as above. First, the ‘turning points’ between the relatively high values of SP and the obvious ‘drop-offs’ in both curves point to Shanghai, Nanjing and Hangzhou producing a maximally balanced regional urban system. This seems to be a straightforward conclusion but can be recast into a broader argument: the three cities are the three main centres within the polycentric urban region. This is consistent with earlier observations (Hall, 1999; Li and Phelps, 2018; Liu et al., 2016) but also recognises that there are, indeed, multiple ‘major’ centres within the YRD. In the YRD agglomeration development plan recently approved by the State Council of China, Shanghai, Nanjing and Hangzhou are positioned explicitly as such regional centres: Shanghai is assigned to assume the function of ‘global city’, with an emphasis on housing advanced producer services and being a financial and innovation centre; Nanjing is assigned to perform the function of regional financial, business services and educational centre; and considering the importance of the high-tech and internet sector, Hangzhou is assigned to assume the function of high-tech centre with innovative e-commerce enterprises. Second, the obvious ‘drop-off’ in the measures of SP implies that adding other cities considerably changes the assumed ‘balance’ among the three main centres. As a corollary, these cities matter (but to a lesser extent) in shaping the polycentric structure of the YRD. The third observation can be gleaned from the trend of remaining stable or slowing down when adding other cities. This can be relatively easily interpreted: continually adding smaller cities – which exhibit a significant gap in importance compared with the cities already added – will not markedly affect the regional structure. This echoes Meijers’ (2008) arguments that often only a handful of large cities determine the extent of mono- or polycentricity.

Investigating mono- or polycentric structures of urban regions along the YREB

In this section, we measure the SP of the other seven urban regions along the YREB from both a morphological and a functional perspective. Figure 4 charts their change patterns, which can be classified into three meta-types.

Figure 4.

Stepwise polycentricity of eight major urban regions along the YREB. YRD, Yangtze River Delta; WJ, Wanjiang cluster; CZT, Changsha–Zhuzhou–Xiangtan cluster; WH, Wuhan cluster; PYL, Poyang Lake cluster; CC, Chongqing–Chengdu cluster; CYN, Central Yunnan cluster; CGZ, Central Guizhou cluster.

The SP of most of these urban regions from a morphological perspective, with the exception of the YRD and the Chongqing–Chengdu cluster, are representative of the first type. Their SP starts from a low initial value and then gradually increases when more cities are added. This implies that the largest city and the second largest city exhibit an obvious imbalance, while the addition of more cities increases the ‘balance’ between the top cities. Clearly, this trend defines a monocentric structure.

The second type is more visible in the Changsha–Zhuzhou–Xiangtan cluster and Wanjiang cluster in their functional polycentricity. Their SP starts from an already high initial value and then fluctuates or grows even further as cities are added. This trend implies that these additional cities are in relative balance with the main city. This, of course, points to a polycentric structure, but with a particular pattern in that there is indeed a rough balance across the entire region.

We can abstract the third meta-type of the change of benchmarked SP from the remaining patterns. Similar to the pattern of the YRD, their SP starts from a high initial value and then drops off when more cities are added, despite some regions showing rising values again further down the line (the Chongqing–Chengdu cluster presents a straightforward example of this). As discussed before, this trend points to a broadly shared regional polycentric structure.

Table 1 lists the three meta-types of the trend of stepwise polycentricity and maps corresponding topologies of regional structures.

Table 1.

Typologies of eight urban regions, trends of stepwise polycentricity and topologies.

Patterns	Examples
	Morphological perspective	Functional perspective
Monocentric urban regions	WJ; PYL; WH; CZT; CYN; CGZ
Polycentric urban regions that consist of cities with similar size		CZT; WJ
Polycentric urban regions that consist of large and small cities	YRD; CC	YRD; PYL; WH; CC; CYN; CGZ

Notes: YRD, Yangtze River Delta; WJ, Wanjiang cluster; CZT, Changsha–Zhuzhou–Xiangtan cluster; WH, Wuhan cluster; PYL, Poyang Lake cluster; CC, Chongqing–Chengdu cluster; CYN, Central Yunnan cluster; CGZ, Central Guizhou cluster.

We are now in a position to explain how the mono- or polycentric patterns in the regions are reflective of the intuitive impression of their regional structures. In morphological terms, all these monocentric urban regions are dominated by provincial capitals. This is in line with the strong political undercurrents in the Chinese urban system (Cartier, 2016). In the context of decentralisation of China’s urban government (Wei, 2001), the administrative levels of cities (such as municipality-level, sub-provincial level, and prefectural level) to some extent represent institutional, governance and policy-making power. This power is closely related to free(r) market policies and statutes, which is a crucial factor for attracting service firms. As a result, high political-level cities such as municipalities and provincial capitals are more likely to be preferred cities when service firms are expanding their office networks, and they more easily play the role of gateway cities to export services within and beyond provincial markets.

In the Chongqing–Chengdu cluster, the pattern of two nuclei is obvious: they have been deemed the twin poles of economic growth in Western China. Obtaining official approval from the central government is an important signal for confirming a city’s central position in regional/national urban systems in China. The Ministry of Housing and Urban–Rural Development (MHURD) of China recently proposed the concept of a ‘National Central City (NCC)’, through which the central government intends to reduce the burden on Beijing and Shanghai of accommodating massive population and promote the development of these NCCs’ surroundings. The connotation of NCC is consistent with the definition of the morphological importance of cities in our research, which focuses on cities’ overall functions of servicing other cities within and beyond the urban regions in which they are located. A couple of cities have been officially/quasi-officially acknowledged to be NCCs, including Beijing, Tianjin, Shanghai, Chongqing, Guangzhou, Shenzhen, Chengdu, Wuhan and Zhengzhou, while Chongqing and Chengdu are the only two NCCs within the same urban region. This, in turn, reflects that most urban regions are monocentric from a morphological perspective, with some exceptions such as the YRD and the CC.

In functional terms, the Changsha–Zhuzhou–Xiangtan cluster is special because all three cities are highly balanced. This is in line with the characteristics of this urban region: it consists of only three cities within a close geographical distance (30-minute commuting time), as well as being orchestrated as a tightly integrated alliance by local governments almost 50 years ago (Tao, 2005). The Wanjiang cluster’s particular pattern of functional polycentricity can be explained in terms of the relative lack of the dominance of Hefei. As an indication of regional dominance, capital cities in Anhui province have gone through different changes since the Qing dynasty, with Anqing, Liu’an, Bengbu, Wuhu and Hefei all being the capital in some periods. The historical heritage of repeated changing of provincial capitals has resulted in its functional polycentricity. In comparison with this, however, its monocentric feature in morphological terms, reflects that provincial capitals are granted strong (political and economic) power in providing for regional and national functions. In other words, multiple centres act as regional headquarters within the province, while Hefei bridges information or capital between regional system and national system, thus playing the function of ‘gateway city’. Other urban regions all have two or three large cities, which function as regional growth poles within provinces or urban regions. An obvious example is the Poyang Lake cluster, which has a conspicuous dual-nuclei functional structure that has been tightly connected by the well-developed Nanchang–Jiujiang (Chang-jiu) industrial corridor with plenty of government-dominated investments (Waters, 1997).

Conclusions

In this paper we analysed the issue of the sensitivity of the ‘level’ of urban polycentricity to the number of centres included in the analysis. We did so by performing a stepwise measurement of the level of polycentricity in the YRD and seven other urban regions, drawing on intercity business connections in China. To enhance the validity of our stepwise measurements, we add a benchmark procedure by comparing these regions with an abstract urban system with a rank-size distribution. The empirical investigation clearly shows that measures of polycentricity are highly sensitive to the choice of centres. As this research is built upon the example of urban regions with large city logic, the significant difference between large cities and small cities in terms of city size in these regions may magnify the sensitivity of polycentricity to the choice of cities. However, this does identify a need for analysing which cities should be included when quantitatively assessing polycentric urban regions. Without such an analysis, any measure of polycentricity will risk being shaped by the choice of cities. Although we focused on the case of polycentric urban regions (and therefore inter-city polycentricity), it can be expected that these findings are also relevant for other forms of urban polycentricity (such as intra-city polycentricity).

Our analysis also shows the additional potential uses of the sensitivity investigation of polycentricity. First, drawing on the examples of the YRD to illustrate, the trend of the benchmarked SP can be used to investigate the different roles that cities perform in shaping regional structures. Second, the change curves of benchmarked SP can also give a ‘deeper’ identification of mono- or polycentric structures of urban regions. Based on the examples of seven urban regions along the YREB, we abstracted three meta-types of change of SP.

This paper focused on the identification of ‘centres’ when measuring ‘urban polycentricity’. This is, of course, an exercise that appears to have a fundamental scientific bearing, but it also has policy implications. In the Chinese context, political decisions on which and how many cities should be incorporated in ‘urban regions’ (or their Chinese planning analogue: ‘urban clusters’) is vitally important. There tend to be two types of delimitations of an ‘urban region’ in China, which represent both different initiators of bundling single cities into urban regions as well as different processes of region-building: (1) a bottom-up process, initiated by local governments; and (2) a top-down process, initiated by the central government (Li and Wu, 2018). On the one hand, to pursue network and agglomeration externalities, neighbouring cities tend to build regional alliances by sharing transport infrastructure, co-building industrial parks, unifying tax and budget systems, etc. Such regional alliances often exhibit a gradual development, stepwise extending their scope to include more cities, and may or may not be post-hoc acknowledged by the central government. Such bottom-up processes of region-building are accompanied by different delimitations of regions produced by local governments in different historical stages. The increasing number of cities in the official Yangtze River Delta Urban Economic Coordination Office is an obvious example here and has led to different delimitations of the YRD. On the other hand, as constructing an urban region is believed to be accompanied by dynamics of economic growth, the central government itself is also taking a key role in integrating cities into an overarching regional structure. For instance, in the national 13th Five-Year Plan (2016–2020), 19 urban clusters are identified, with 90% of future economic growth said to be taking place in these regions. Delineating these urban regions requires a consideration of the effective coordination involving different levels of government, the reduction of regional disparities and the integration of physical infrastructure. As a result, PUR-like structures designated as such by the central government do not really follow a specific and consistent pattern: such urban regions tend to be the product of a balance of interests among different levels of government more than anything else. Taken together, then, the ‘political’ selection of cities in building such putative PURs mix different motivations, are put forward by different initiators and therefore produce very different types of PURs. This implies that it is questionable whether these urban regions are uniformly rooted in regional integration through intercity networking. This also implies that in practices of policy making and regional planning, analyses of how many and which cities are needed to be able to speak of a ‘fair’ degree of integration are relevant. In light of this, the current paper offers a potential tool.

Alongside the identification of what constitutes a ‘centre’, the geographical scale of analysis also affects measures of ‘urban polycentricity’. A PUR may seem to be monocentric if measured through global-scale interactions and polycentric if measured through national or regional-scale interactions. This is because international service firms tend to concentrate in a limited number of leading cities (e.g. only in Shanghai), while national service firms may locate even in the smallest cities. Empirical analyses of the multiscalar nature of external urban service linkages of Chinese cities have, for example, indeed shown a less hierarchical structure at the regional and national scale than at the global scale (Zhang and Kloosterman, 2016; Zhao et al., 2015). In the context of the measurement of polycentricity, this scale-dependence, together with the sensitivity of polycentricity to the identification of ‘urban centres’ as well as to the concrete measurement methods (see Marcińczak, 2019), suggests that the analysis of polycentricity remains fragmented and intricate.

As a methodological and empirical exploration, this paper of course has some limitations, which at the same time suggest avenues for further research. The first concerns how the units of analysis are defined. The selection of the number of cities cannot be explored independently from the issue of what constitutes a city, especially not in areas where urbanisation is nebular and centre identification becomes an issue in its own right. Although this paper is set up as a specific exploration of the basic question of the number of cities when assessing urban polycentricity, discussing a broader question of unit selection would be an obvious area for future research. Second, the question as to which cities should be included has remained fuzzy. For instance, because the ‘turning point’ in the measurement of benchmarked SP allows identifying the most ‘important’ cities in shaping polycentric structures, here it is viewed as a meaningful indicator to quantify the extent of polycentricity. This, however, requires further theoretical and empirical verification. The point we argue here is that, in any case, the selection of cities when assessing polycentric urban regions should be on the basis of the investigation of the sensitivity of polycentricity. Third, there are of course various indices to define the importance of cities: for example, following a social network approach, we can employ betweenness centrality, eigenvector centrality or degree centrality – the index we used in this paper – to measure the roles of cities, and different measures represent different understandings of positionality in urban networks. Examining other measures of centrality would enrich our understanding of how cities play different roles and how these add up to PUR-formation (or not). Furthermore, although the GaWC approach provides an often-used approach to generating intercity connections, other analyses using other approaches or data (e.g. Shi et al., 2019) may produce complementary observations on polycentric structures.

Footnotes

Acknowledgements

The authors are very grateful for the insightful comments and suggestions made by the editor and anonymous reviewers. All remaining errors are the authors’ own.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The first author is thankful for the financial support from the Fundamental Research Funds for the Central Universities (Grant number: 2018ECNU-HWFW029; 2018ECNU-HLYT016); Shanghai Philosophy and Social Sciences Fund (Grant number: 2018ECK009); and the Major Projects of Humanities and Social Sciences Key Research Base of Ministry of Education (Grant number: 17JJD790007).

Notes

ORCID iDs

Weiyang Zhang

Ben Derudder

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