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W. Zhang, B. Derudder, J. Wang, F. Witlox / Bulletin of Geography. Socio-economic Series / 31 (2016): 145–160

153

geographic concentration of passenger flows along 

the Nanjing-Shanghai-Hangzhou-Ningbo belt, 

where the main HSR lines lie, i.e. Shanghai-Nan-

jing HSR line, Shanghai-Hangzhou HSR line and 

Hangzhou-Ningbo HSR line. In addition, Shanghai, 

Nanjing and Hangzhou emerge as the most con-

nected cities in the network of passenger flows; Su-

zhou (one of the most dynamic cities that attract 

foreign direct investment in YRD (Zhao, Zhang, 

2007)), Ningbo (the main gateway city in the south-

ern part of the YRD) and Hefei (the administra-

tive and economic centre of Anhui province that 

has been looking to join the YRD regional collec-

tive) are three sub-centre nodes of the network of 

passenger flows.

4.2. Comparison 

between the original network generated  

by the proxy of the number of daily trains 

and the transformed network

Our alternative approach is devised to address the 

obstacle of overly flat structures produced by train 

schedule-based methods for assessing urban net-

works. Here, we examine the changes put forward 

by applying the transformation set out in section 3 

by comparing original and transformed networks at 

the level of nodes, linkages, and network structures.

We first offer a direct comparison of cities’ 

degree centralities in both networks (fig. 3). Degree 

centrality is a measure of nodes’ position, which 

represents the (valued) number of passenger flows 

of cities. The first obvious change to note is that 

the degree centralities of a range of cities, which 

can be separated into two categories, seem lower 

in the transformed network. The first category 

is Nanjing, the sub-center city within the YRD. 

There are 444 HSR trains operating across Nanjing 

on a daily basis, which is almost the same as the 

number of HSR trains operating across Shanghai 

(490 per day). However, part of these trains only 

transit across Nanjing, while most of them depart 

from or have their final stop at Shanghai. That 

means Shanghai contributes most of the passen-

gers, whereas Nanjing only contributes part of the 

passengers. In this case, Nanjing’s position in the 

original network is obviously overestimated. The 

other category includes Suzhou (Jiangsu), Wuxi, 

Changzhou, Zhenjiang, Shaoxing, and Xuzhou, 

which are transit cities in main corridors: Suzhou 

(Jiangsu), Wuxi, Changzhou, and Zhenjiang are on 

the Shanghai-Nanjing HSR railway line, Shaoxing 

is on the Hangzhou-Ningbo HSR railway line, and 

Xuzhou is on the Beijing-Shanghai HSR railway 

line (fig. 1). This is consistent with the theoretical 

illustration of over-estimations of the position of 

transit cities in section 2.2. On the other hand there 

are also nodes becoming relatively more important 

in the transformed network. The most dramatic 

change is the higher rankings of Hefei, Ningbo, 

Hangzhou and Wenzhou.

Second, fig. 4, in which edge thickness reflects 

the flow strength of city-pairs, maps the 15 most 

connected city-dyads in the original network as well 

as the transformed network. City-dyads along the 

Nanjing-Shanghai HSR line are the most connected 

city-dyad—with the exception of Shanghai-Hang-

zhou—in the original network (fig. 4a). This reflects 

the fact that any pair of cities along the Shang-

hai-Nanjing HSR line will have similar number of 

inter-city trains. Compared with the pattern of con-

centrating on the Shanghai-Nanjing corridor in the 

original network, the backbone of the transformed 

network (fig. 4b) consists of the key cities along the 

Nanjing-Shanghai-Hangzhou-Ningbo belt, which is 

more consistent with the central corridor of YRD 

urban agglomerations (Gu et al., 2007). More spe-

cifically, the original network tends to overvalue 

inter-city connections, such as Nanjing-Wuxi and 

Shanghai-Zhenjiang, along the Nanjing-Shanghai 

HSR line, but on the other hand there are also in-

ter-city connections that are being undervalued. 

These connections can be divided into two simple 

categories: the connections between Shanghai and 

sub-centers that are not on the Shanghai-Nanjing 

corridor (i.e. Hangzhou, Ningbo and Hefei), and the 

connections between pairs of proximate sub-centers 

(i.e. Nanjing-Hefei, Hangzhou-Ningbo). In  the lat-

ter cases, the dense flows of people between Nanjing 

and Hefei—the closest pair of provincial capitals 

in China—are apparent, especially in the context 

of the regional integration of Yangtze Economic 

Zone. The Hangzhou-Ningbo corridor, along which 

long-running and dynamic peri-urbanization pro-

cess has occured (Webster, Muller, 2002), typifies 

the cooperative pattern of core city (Hangzhou) and 

sub-centre & port city (Ningbo): Ningbo—Hang-

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W. Zhang, B. Derudder, J. Wang, F. Witlox  / Bulletin of Geography. Socio-economic Series / 31 (2016): 145–160

154

Fig. 3. Cities’ degree centralities in the original network and the transformed network

Source: Own studies

zhou’s vicinity having more attractive labor, land 

and tax costs—attracts many manufacturing func-

tions to moving from Hangzhou with keeping R&D 

and sales functions in Hangzhou (Webster et al., 

2003); on the other hand, Ningbo’s deep-sea con-

tainer port provides Hangzhou with more wide in-

ternational market and hinterland. This provides 

fundamental bases for the dense inter-city flows be-

tween Hangzhou and Ningbo.

And third and finally, to explore the structural 

difference between both networks, we compare the 

rank-size distributions of cities’ degree centralities. 

The posited flatter structure of the original network 

is indeed shown by the much steeper drop-off in the 

cities’ degree centralities in the transformed network, 

shown in fig. 5. We calculate the integration of rank-

size curve of cities’ degree centralities to measure 

the flat degree of both networks. After normalizing 

cities’ ranks into the interval [0,1], the flattening 

ratio (F) of networks can be calculated as:

 

1

0

( )

F

L X dX

=

∫

F= (11)

where the function Y = L(X) represents the rank-

size curve. The flattening ratio varies between 0 for 

completely even and 1 for completely uneven net-

works. In our measures, the flattening ratio of the 

original network (0.39) is much higher than the 

flattening ratio of the transformed network (0.23): 

more precisely, the flattening ratio of the trans-

formed network has decreased to 60% of the origi-

nal flattening ratio in the case of the HSR network 

within the YRD.

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