Differentiating Centrality and Power in the World City Network
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48(13) 2733–2748, October 2011
Differentiating Centrality and
Power in the World City Network
Zachary Neal
[Paper first received, July 2010; in final form, September 2010]
Abstract
Centrality and power have become common foci for world city network research
and frequently serve as tools for describing cities’ position or status in the system.
However, these concepts are difficult to define and measure. Often they are treated as
equivalent: more central cities have more power. This paper challenges this assumed
equivalence by proposing conceptually distinct definitions and developing two new
measures that allow them to be differentiated empirically. Applying the proposed
measures in a hypothetical world city network and the Internet backbone network
reveals that centrality and power are distinct and suggests that world cities should be
viewed as arising from multidimensional network positions that define multiple types:
quintessential world cities that are both central and powerful (such as New York and
London), hub world cities that are central but not powerful (such as Washington and
Brussels) and gateway world cities that are powerful but not central (such as Miami
and Stockholm).
Recent research on world urban systems 2006). However, these concepts are difficult
has been characterised by a shift away from to define and measure. The most common
viewing cities as hierarchically organised approach to measuring a city’s centrality in
and towards conceptualising the system the world city network involves counting
as a network of intercity relations: a world its total number of relationships or net-
city network. As a result, such intrinsically work connections. Yet, do all relationships
relational constructs as centrality and power contribute equally to a city’s centrality, or
have become common foci of interest and are some relationships more valuable than
frequently serve as tools for describing cit- others? Similarly, it is often assumed that
ies’ position or status in the system (see cities occupying more central positions in
for example, Smith and Timberlake, 2001; the world city network are more powerful
Alderson and Beckfield, 2004; Choi et al., and able to control or influence the flow of
Zachary Neal is in the Department of Sociology, Michigan State University, 316 Berkey Hall East
Lansing, Michigan, 48824-1111, USA. E-mail: zpneal@msu.edu.
0042-0980 Print/1360-063X Online
© 2010 Urban Studies Journal Limited
DOI: 10.1177/00420980103889542734 ZACHARY NEAL
resources (for example, Taylor, Walker et al. third section demonstrates the utility of these
2002; Alderson and Beckfield, 2004; Alderson new measures by applying them to hypotheti-
et al., 2010; Ma and Timberlake, 2008). Yet, cal and observed world city networks. The
is power a consequence of centrality, or are paper concludes with a discussion of the
these two relational constructs distinct? More implications of cities’ centrality and power, as
than simply an issue of methodology and defined in the proposed ways, on processes of
language, a robust set of concepts and tools globalisation and world city formation.
for describing cities’ relationships is essential
for understanding the world city network and Background
world city formation.1
To provide a framework for answering such At least since Friedmann’s (1986) world city
questions, this paper explores the relationship hypothesis, the notions of centrality and
between centrality and power, and develops power have featured prominently in discus-
an approach for their measurement and dif- sions of world cities and the world city net-
ferentiation. First, viewing centrality in the work. Indeed, it would be quite surprising to
world city network as a force that concentrates find a paper in this body of literature that did
resources or allows them to be efficiently dif- not use both terms at least once. However,
fused, a recursive conception of centrality is they are often used in loose or imprecise
proposed wherein a city’s centrality depends ways that challenge their utility as analytical
on the centrality of the cities to which it is tools.2 In this section I briefly consider how
connected. Secondly, viewing power in the these concepts have been used as theoretical
world city network as the ability to control constructs and how they have been measured
resource flows between cities, a similarly in empirical applications.
recursive conception of power is proposed Centrality, as applied to cities in the context
wherein a city’s powerfulness depends on the of globalisation and world city networks, has
lack of centrality of the cities to which it is con- been identified as the catalyst for two related
nected. These two measures are applied to two but opposite processes: concentration and
different world city networks: the hypotheti- diffusion. First, centrality has been used to
cal network described by Friedmann (1986) denote the concentration of resources in par-
that initiated the earliest research in this area; ticular cities or, more accurately, the structural
and, the Internet backbone network origi- arrangement of resource flows that facilitate
nally analysed by Choi et al. (2006). Results such concentration. Friedmann’s world city
suggest that centrality and power are theo- hypothesis argued that
retically and empirically distinct constructs
key cities throughout the world are used by
worth differentiating and that the proposed
global capital as basing points [and that] world
measures identify positional characteristics cities are major cites for the concentration
missed by more traditional measures. and accumulation of international capital
This paper is organised in four sections. The (Friedmann, 1986, p. 73).
first section briefly reviews how the concepts
of centrality and power are currently dis- These interrelated hypotheses highlight
cussed and measured in world city network how centrality—that is, being enmeshed in
research. In the second section, an alternative exchanges of resources or in what Castells
approach to measuring centrality is developed (1996) called the ‘space of flows’—is a driving
that draws on theories of social capital, and force behind the emergence of world cities.
a related measure of power is developed that Sassen (2010) further developed these ideas by
draws on theories of social exchange. The noting that, as networks serve to concentrateDIFFERENTIATING CENTRALITY AND POWER 2735
resources in particular places, new forms of sites where innovations and reputation can
territorial centrality arise, including not only be spread rapidly and widely throughout
the traditional downtown business centre, the network. In this paper, although I do not
but also the suburbs as emerging centres of distinguish between its roles facilitating the
global finance. Indeed, although some have concentration and diffusion of resources, I
suggested that networks of transport and do adopt a specifically structural conception
communication have reduced the importance of the source of cities’ centrality: each city’s
of place by creating a ‘flat world’ (Friedman, centrality is a function of its position within
2005), it is far more likely that these networks, the world city network.
through their ability to concentrate resources Together with centrality, power is a domi-
in highly central cities, have exacerbated the nant concept in the study of world cities, but
unevenness of the global urban landscape one that is difficult to address with precision
(Florida, 2005). Thus, in many instances, because it has been used in such diverse ways.
cities’ centrality within a world city network is Noting that cities are key sites for multina-
viewed as a new mechanism for capital accu- tional corporate headquarters, some con-
mulation where a central location in space is nect cities’ power to their roles as centres of
augmented by a central location in networks command-and-control in the global economy
of resource exchange. (Sassen, 1991). Others view cities as powerful
However, centrality has been used to describe to the extent that they can dominate other
the structural arrangement of resource flows cities, whether via traditional world systems
that facilitate the diffusion of ideas, capital dichotomies (Friedmann, 1986; Derudder
and people. That is, a central position in the et al., 2010), or through the structure of global
world city network can lead not only to the supply chains (Hesse, 2010). Still others, who
concentration of resources within a city but, adopt an actor–network theory approach,
by providing a city with a wider reach, can view power as systemic rather than concen-
also lead to the efficient diffusion of those trated in individual cities. For example, Allen
resources throughout the network. Adopting argues that
a diffusion view of centrality, Wheeler and
power does not radiate out from any given
Mitchelson (1989) examined the flow of
centre, as much as it runs along the length and
information among US cities as indicated by breadth of a network (Allen, 2009, p. 203; see
Federal Express shipments, finding that com- also Grewal, 2008).
monly cited examples of American world cit-
ies (New York, Chicago, Los Angeles) were key This proliferation of conceptions of power has
sites of information creation and dissemina- led to the development of several typologies
tion, rather than information concentration. of power (Allen, 1997, 2009) and has forced
These cities’ ability to ‘get the word out’ was researchers to employ “an eclectic theoretical
facilitated by their central position within the position” that attempts to merge these into a
Federal Express network. Similarly, centrality unified idea (Taylor, 2004, p. 88). Thus, it is
within air traffic networks allows some cities important to be clear what version of power
to deliver business services more effectively to I intend to address. In this paper, I focus on
increasingly global hinterlands (Neal, 2010a, what Dahl (1957) initially described as ‘power
2010b). Often, these two aspects of central- over’ and what Allen (1997) later described as
ity—concentration and diffusion—intersect ‘power as a capacity’. This approach equates
to provide cities with a double structural power with an ability to dominate and con-
advantage, as sites where capital converges trol, and views the fact that some cities are
and collects from many sources, but also as more able to influence the circulation of2736 ZACHARY NEAL
resources through the world city network follow this approach, assessing power in light
than others as fundamental to their status as of other measures of centrality applied to dif-
world cities. Additionally, as with centrality, ferent data, including flow centrality in office
I adopt a specifically structural conception of networks (Wall and van der Knaap, forth-
the source of cities’ power: each city’s power coming) and eigenvector centrality in airline
is a function of its position within the world networks (Mahutga et al., 2010). Similarly,
city network (see Neal and Neal, 2010). in analyses of the interlocking branch office
Although multiple conceptions of both networks, a single measure called ‘network
centrality and power in the world city net- connectivity’ is used in some cases to measure
work exist, there appears to be consensus cities’ centrality (Beaverstock et al., 2002) and
that these two concepts are closely related. in other cases to measure their power (Taylor,
More specifically, it is generally assumed Walker et al., 2002).
that cities occupying central positions in the However, theories of social exchange have
world city network—positions that facilitate questioned the relationship between central-
the concentration of resources in, or diffu- ity and power. Emerson (1962) argued that
sion of resources from, the city—are more power derives not simply from one’s having
powerful. Those cities that are densely inte- a large number of relationships (i.e. being
grated into the intercity economic, political central), but specifically from having rela-
or social flows (i.e. centrality) enjoy access tionships with dependent others. Drawing
to concentrated pools of resources and the on these ideas, Cook et al. (1983) found
ability to diffuse those resources widely, which that, when actors are engaged in economic
in turn provides opportunities to exercise exchange, those whose exchange partners
control over them (i.e. power). Thus, in most are dependent upon them (i.e. who were in
discussions of world cities and the world city positions of power) had more opportuni-
network, centrality and power are treated as ties to control and influence exchanges than
equivalent, or at least causally linked: power is did those who merely had a large number
derived from a central network position. The of opportunities to exchange (i.e. who were
conflation of centrality and power is clear in in positions of centrality). That is, central
theoretical discussions. For example, Allen actors may enjoy many opportunities to
argues that exchange resources, but they have relatively
little opportunity to exercise power over those
powerful cities ... stand at the intersections,
exchanges. In contrast, powerful actors may
so to speak, of all that matters in global
economic terms (Allen, 2009, p. 187). have few opportunities to exchange, but they
exercise a great deal of influence over those
Thus, he connects power to the extent to opportunities that do exist. This finding sug-
which a city lies at the centre of several con- gests that positions of centrality are distinct
verging resource flows. Similarly, Boschken from positions of power and have different
(2008, pp. 8–9) describes centrality as “based consequences.
in part on the city’s role as a node of power Before turning to the question of whether
and connectivity”. These concepts are often centrality and power should be treated as
used interchangeably in empirical analyses as conceptually and empirically distinct in
well. Alderson and Beckfield (2004, p. 822), investigations of world cities, it is useful to
for example, note that in examining corporate consider how cities’ centrality has actually
networks “we assess the power of world cities been measured in past studies. The earliest
in light of three measures of point centrality” studies of cities’ centrality did not directly
(see also Alderson et al., 2010). Others also examine position within a network of cities,DIFFERENTIATING CENTRALITY AND POWER 2737 but rather used cities’ internal features as a While degree centrality offers a straightforward proxy indicator of centrality: comprehensive way of measuring the extent to which cities’ political-cultural-financial indices (Hall, are highly connected, two conceptual chal- 1966; Reed, 1981), counts of headquarters lenges arise. First, using a single measure to and corporate service firms (Friedmann, assess both cities’ centrality and their power- 1986; Sassen, 1991) and even occurrences fulness does not allow the possibility for these of major spectacles like the Olympics or the two characteristics of cities’ position in the 1995 Rolling Stones World Tour (Short et al., world city network to be distinct; it ignores 1996). Hierarchical rankings of cities based on the possibility that some cities are central, these features were assumed to mirror cities’ while others are powerful.3 Secondly, simply centrality in an unobserved intercity network counting up a city’s total number of connec- because they indicate the consequences of tions in the network implicitly assumes that such positions of centrality. This approach each connection is equally valuable, when in is problematic, however, because it risks an fact some connections (for example, to New inherent circularity: the presumed effect of York) may be more valuable than others (for centrality in the world city network is used example, to small, local towns). as an indicator of centrality itself. A limited number of studies have used more Among those empirical studies that directly sophisticated measures of centrality known examine the world city network, the most as closeness and betweenness (Alderson and widely employed measure of centrality Beckfield, 2004; Alderson et al., 2010; Neal, involves counting a city’s total number 2008). Closeness centrality captures the of linkages. In the social network analysis extent to which a city is directly connected to literature, this is known as degree centrality other cities in the network or separated from (Freeman, 1978/79), but other labels have them by only short indirect linkages, reflect- been applied in studies of world cities, includ- ing the notion that both direct and indirect ing interlock connection, nodal connection, linkages contribute to a city’s centrality and situational status (Taylor, 2001) and global to opportunities for capital accumulation connectivity (Taylor, Catalano and Walker, or innovation diffusion. Betweenness cen- 2002). This approach has been used to mea- trality focuses on the extent to which a city sure the extensiveness of cities’ linkages in serves as an intermediary that facilitates the world city networks based on the interlocking flow of resources between other cities in the branch office networks of advanced producer network, reflecting the notion that broker- service firms (Taylor, Walker et al., 2002), ing or gatekeeping positions provide a city corporate headquarters and subsidiary rela- with a unique ability to monitor and control tions (Alderson and Beckfield, 2004; Alderson resource flows. While these two alternative et al., 2010), and air traffic (Ma and Timberlake, approaches to measuring centrality provide 2008). In each case, this measure of centrality different views of cities’ positions in the world is interpreted as an indicator of power and city network, their usefulness is severely lim- thus the two concepts are treated as both ited by the fact that they can only be applied conceptually and empirically equivalent. For to binary networks. That is, cities’ closeness example, Ma and Timberlake argue that and betweenness can only be assessed in one of the most effective measures of network networks where a relationship between cities members’ relative centrality or power either does or does not exist, but cannot be potential is their degree: the number of ties applied to networks where some relation- from and/or to others (Ma and Timberlake, ships are known to be stronger than others. 2008, p. 26). Measures of centrality based on eigenvectors
2738 ZACHARY NEAL
have also been employed (for example, Smith
and Timberlake, 2001; Mahutga et al., 2010),
but are similarly subject to severe limitations,
which are discussed in greater detail in the
following section.
Measuring Centrality and Power
Much progress has been made in the empiri-
cal investigation of world city networks over
the concept’s long history, but these efforts
remain challenged by the conceptual and Figure 1. Two hypothetical world city
networks.
methodological shortcomings of existing
analytical tools. Although notions of cities’
centrality and power are widely used, these connections in both networks. The key dif-
concepts are often left ambiguous or treated ference is that these connections are more
interchangeably, and are measured with valuable in network A because they provide
instruments that do not always match the indirect access to still more cities, while in
theoretical ideas they are intended to assess. network B they are ‘dead ends’. This logic is
In this section, I propose new conceptions closely connected to Bourdieu’s notions of
of centrality and power in the world city social capital depending not only
network, with accompanying measurement
tools, that aim to overcome these difficulties. on the size of the network of connections
Figure 1 depicts two possible city networks, [one] can effectively mobilize [but also] on
the volume of the capital (economic, cultural,
where circles represent cities and lines repre-
or symbolic) possessed in his own right by
sent resource flows between them. While these each of those to whom [one] is connected
two networks have very different structures, (Bourdieu, 1986, p. 249).
the focal city identified by the Black circle has
the same degree centrality (i.e. the same num- Thus, while a focus on only direct connections
ber of direct connections: three) in both cases. suggests that the focal city is equally central
Similarly, the focal city is the most central city in these two networks, taking a wider view
in both networks when using closeness and reveals that it is better positioned in network
betweenness measures of centrality. Thus, A because it is not merely well connected
for the set of three most commonly used itself, but is well connected to others who are
measures of centrality—degree, closeness also well connected. Because this conception
and betweenness (Freeman, 1978/79)—these of centrality depends not only on a city’s own
two networks and the focal city’s position connections, but also on the centrality of the
within them are virtually indistinguishable. other cities to which it is connected, I call it
It is important to consider, however, whether recursive centrality.
there are differences between network A and Because such a position of recursive central-
network B in the focal city’s role as a site of ity increases opportunities for the concentra-
resource concentration and diffusion (i.e. its tion of resources from many sources or the
centrality) and in its role in controlling the diffusion of resources to many sources, it may
flow of resources (i.e. its power). seem reasonable to assume that a recursively
Turning first to centrality, it is clear that the central city is quite powerful. However, exper-
focal city enjoys the same number of direct imental research on agents’ ability to controlDIFFERENTIATING CENTRALITY AND POWER 2739
the flow of resources in exchange settings has they distinguish centrality and power as
demonstrated that centrality does not auto- potentially different features of a city’s posi-
matically translate into power (Cook et al., tion within a network. In network A, the focal
1983). While the focal city in network A has city is central but not particularly powerful,
direct and indirect access to resources from while in network B, the focal city is powerful
a number of sources, so too do the cities to but not particularly central. Differentiating
which it is connected. Thus, the focal city lacks these two characteristics of network position
the ability to control or influence resource reveals that structural arrangements facilitat-
exchanges with its exchange partners. These ing resource accumulation or diffusion do not
partners have alternatives and thus they can necessarily also facilitate resource control,
ignore the actions or demands of the focal city. and vice versa. Some cities may have struc-
In contrast, although the focal city in network tural opportunities to become sites of large
B has access to resources from a more limited concentrations of resources or efficiently to
pool of contacts (i.e. it is not recursively diffuse resources throughout the rest of the
central), it has significant bargaining and network, but little ability to control their
negotiating influence over its exchange part- flow. In contrast, others may have structural
ners because it is their only source for capital, opportunities to control the flow of resources,
information and other valuable commodities. but a limited capacity to accumulate or dis-
These partners have no alternatives and thus seminate them.
cannot ignore the focal city’s demands. Allen These simple networks help to illustrate
touched on the advantage of such a position, the recursive conceptions of centrality and
noting that the importance of such cities as power. However, to be useful in empirical
New York and Tokyo stems investigations of world city networks, these
concepts must be accompanied by practical
from the fact that the world of banking and
measurement methodologies. If the struc-
finance seems to have little choice other than
to go through the financial districts of those ture of a world city network is represented
cities (Allen, 1999, p. 187). in a symmetrical matrix R, where each entry
Rij contains the strength of the connection
This logic is also closely connected to social between cities i and j, then the recursive cen-
exchange theory, which views power as a type trality (RCi) and recursive power (RPi) of city
of relationship in which one agent is able to i can be computed as
dominate others because these others have
RCi =∑ Rij × DC j (1)
limited alternatives (Emerson, 1962). Because j
this conception of power depends not only
Rij
on a city’s own connections, but also on the RPi = ∑
DC j
connections (or, indeed, lack thereof ) of
j (2)
the cities to which it is connected, I label it
recursive power. where, DC j is the degree centrality of city j.
These recursive conceptions of centrality The first equation, used to compute recur-
and power offer two significant conceptual sive centrality, sums the total number (or
advantages over existing approaches. First, strength) of city i’s connections, weighting
they do not simply focus on a city’s own con- each one by the degree centrality of the city
nections, treating each as equally useful, but to which it is connected. The second equation,
take a broader view of the world city network’s used to compute recursive power, performs
structure to consider direct connections as the same operation but weights each connec-
well as the status of those contacts. Secondly, tion by the contact’s inverse degree centrality,2740 ZACHARY NEAL thus capturing the extent to which city i is are considered further in the following section, able to dominate (i.e. is the sole exchange in the context of the analysis of specific world partner for) city j (Neal and Neal, 2010). city networks where they arise. These measures can be computed using the command in STATA, which has been written to accompany this paper; it can Applying Recursive Centrality be downloaded by typing ‘findit centpow’ in and Power the STATA command line. Applying these to the hypothetical networks in Figure 1, the Friedmann’s ‘Basing Points’ Network focal city in network A has a high recursive The world city network described by centrality score (9), but a low recursive power Friedmann (1986), while intended only as score (0.75). In contrast, the focal city in a heuristic rather than explanatory model, network B has a relatively lower recursive offers an opportunity to illustrate the pro- centrality score (3), but a relatively higher posed recursive conceptions of centrality and recursive power score (3). These differences power in a relatively simple and well-known highlight the differing positions of these two context (see Figure 2). Table 1 lists each city’s focal cities, despite their equal degree central- score using the traditional degree centrality ity scores. measure, as well as the recursive central- The logic underlying these proposed con- ity and recursive power measures already ceptions of centrality and power is closely described. Eigenvector-based measures related to two existing measures: eigenvector including eigenvector centrality (Bonacich, centrality (Bonacich, 1972) and beta central- 1972) and beta centrality (Bonacich, 1987) ity (Bonacich, 1987).4 Although these have are not appropriate because the network’s sec- been applied in a limited number of world ond eigenvalue (l2 = 3.45) is relatively large city network studies (Smith and Timberlake, compared with its first eigenvalue (l1 = 4.59). 2001; Choi et al., 2006; Mahutga et al., 2010), This mathematical property typically occurs their computation is complex, involving an in networks where clustering or cliqueishness analysis of the network matrix’s eigenvectors. is present. In this case, regional clusters of Additionally, their usefulness in examining Asian, North American and European cit- world city networks is limited by two impor- ies are clearly visible. Using such measures tant constraints that are often overlooked. in clustered networks can yield results that First, they cannot be applied to networks that focus only on the largest cluster, and is akin contain clustering or cliques, which are com- to examining only the first factor in a factor mon in world city networks (Derudder et al., analysis even if subsequent factors were also 2003; Derudder and Taylor, 2005). Secondly, found to be important. they often do not yield useful results when Comparing the results of the recursive applied to networks that are large (for exam- measures with those of the more traditional ple, 3692 cities in Alderson and Beckfield, degree centrality measure, it is clear that the 2004) or contain many strong linkages (for recursive measures provide finer-grained example, London’s degree centrality is 63 399 distinctions among cities. Using degree in Taylor, Catalano and Walker, 2002). The centrality, many cities are tied with the same mathematical complexity of eigenvector cen- scores; among the 25 cities in the network, trality (Bonacich, 1972) and beta centrality there are only seven unique degree central- (Bonacich, 1987) places a detailed discussion ity scores. This suggests, for example, that of their computation and properties beyond Los Angeles, Tokyo and Singapore are struc- the scope of this paper, but these limitations turally identical because they have the same
DIFFERENTIATING CENTRALITY AND POWER 2741 Figure 2. Friedmann’s world city network. Table 1. Comparing centrality and power among Friedmann’s world cities Degree centrality Recursive centrality Recursive power Los Angeles 1.00 Los Angeles 1.00 Paris 1.00 Tokyo 1.00 Tokyo 0.88 Singapore 0.85 Singapore 1.00 Singapore 0.82 Tokyo 0.80 Chicago 0.86 Chicago 0.76 London 0.78 New York 0.86 New York 0.73 New York 0.67 London 0.71 Rio de Janiero 0.70 Rio de Janiero 0.65 Rio de Janiero 0.71 Sydney 0.64 Chicago 0.64 Mexico City 0.57 San Francisco 0.61 Los Angeles 0.63 Miami 0.57 Mexico City 0.58 Miami 0.40 Paris 0.57 London 0.55 Hong Kong 0.36 Hong Kong 0.43 Miami 0.55 Taipei 0.36 Houston 0.43 Houston 0.52 Mexico City 0.34 San Francisco 0.43 Manila 0.42 Houston 0.21 Sydney 0.43 Hong Kong 0.36 Bangkok 0.18 Taipei 0.43 Taipei 0.36 Seoul 0.18 Bangkok 0.29 Toronto 0.36 Madrid 0.17 Caracas 0.29 Bangkok 0.30 San Francisco 0.17 Madrid 0.29 Caracas 0.30 Sydney 0.16 Manila 0.29 Seoul 0.30 Caracas 0.15 Seoul 0.29 Madrid 0.27 Toronto 0.12 Toronto 0.29 Paris 0.27 Manila 0.11 Buenos Aires 0.14 Buenos Aires 0.15 Milan 0.09 Johannesburg 0.14 Johannesburg 0.15 Vienna 0.09 Milan 0.14 Milan 0.12 Buenos Aires 0.07 Vienna 0.14 Vienna 0.12 Johannesburg 0.07 Notes: Ties are listed in alphabetical order. Scores are rescaled with a maximum value of 1. number of linkages to other cities. In con- the 25 cities, there are 17 unique recursive trast, using recursive centrality and power, centrality scores and 20 unique recursive there are fewer cities with tied scores; among power scores. Thus, the recursive measures
2742 ZACHARY NEAL allow cities’ positions in the network to be The Internet Backbone Network distinguished more effectively. For example, Although applying the proposed recursive the recursive centrality measure reveals that centrality and power measures to Friedmann’s although Los Angeles, Tokyo and Singapore hypothetical world city network is instructive, may have the same number of direct link- it is also important to consider how these ages, Los Angeles is likely to enjoy greater measures work when applied to ‘real’ data. concentrations of resources and greater Examining the network of Internet backbone ability to disseminate innovations than the connections among cities—the physical other two. infrastructure that digitally links cities to one In addition to allowing finer-grained dis- another—offers an opportunity to examine tinctions among cities’ network positions, the directly one actual world city network. Choi recursive measures also allow cities’ centrality et al. (2006) compiled a network of 82 inter- and power to be considered separately. Using national cities from two annual reports of degree centrality, Paris appears to be moder- Internet geography (Telegeography, 2002a, ately central (0.57), which may be interpreted 2002b) and have kindly provided their data as evidence of second-tier world city status. for this paper. Unlike the Friedmann network However, a more complete picture of Paris’ already considered, which merely indicated world city status emerges when centrality and the presence or absence of a relationship, this power are treated as distinct concepts. Paris network captures the capacity for informa- has a relatively low recursive centrality score tion flow between pairs of cities, measured as (0.27), but has the highest recursive power megabits per second (Mbps) of bandwidth. score in the network (1.0). These results Like all networks among cities, the organisa- might suggest that, while Paris may not be a tion of the Internet’s physical infrastructure hub of capital accumulation, it is a centre of is the result of some combination of political command-and-control, serving as an inter- forces and a cost-minimising logic of growth. mediary that connects other European cities Yet, whatever the causes of its current struc- (such as Milan, Vienna) to the world. That ture, it remains the principal method for is, to view Paris as a second-tier world city moving information between cities and thus obscures its more nuanced role as a minor is of critical importance for economic, social, site of flow concentration but a major site of political and cultural activities. Beyond its role flow influence. A similar but reversed story in structuring a range of intercity transac- emerges in the case of Sydney which, like tions, I examine this Internet infrastructure Paris, appears moderately central using degree network data for two additional reasons. First, centrality (0.43) but, unlike Paris, is revealed it is relational data that directly measure rela- to be highly central (0.64) and minimally tionships between pairs of cities, rather than powerful (0.16) when the recursive measures the more common attribute data that mea- are used. The cases of Sydney and Paris mir- sure characteristics of individual cities such ror the cases of the focal cities in Figure 1’s as the presence advanced producer service network A and network B. Despite both cit- firms (Taylor, Catalano and Walker, 2002) or ies having similar degree centrality, Sydney’s multinational headquarters data (Alderson position in the Friedmann network closely and Beckfield, 2004; Alderson et al., 2010; for resembles the ‘central but not powerful’ focal a critique, see Nordlund, 2004; Neal, 2010a). city in network A, while Paris’ position more Secondly, it was originally analysed in a highly closely resembles the ‘powerful but not cen- cited study of world city networks (Choi tral’ focal city in network B. et al., 2006) using eigenvector-based measures
DIFFERENTIATING CENTRALITY AND POWER 2743 of centrality and power that are conceptually and highly powerful. In this case, recursive similar to those proposed earlier, but which centrality indicates that these cities have many were methodologically inappropriate. Thus, high bandwidth connections to cities that the discussion that follows might be viewed themselves also have many high bandwidth as a re-analysis that provides a more robust connections. Such a position allows large assessment of cities’ centrality and power. amounts of information, coming both from In this case, eigenvector-based measures direct connections as well as more distant like eigenvector centrality (Bonacich, 1972) indirect connections, to converge in a single and beta centrality (Bonacich, 1987) are not location and allows large amounts of infor- appropriate because the network’s largest mation to be diffused very efficiently from eigenvalue (l1 = 178 231.55) is too large. This London and New York to the rest of the world. typically occurs in networks with many nodes This provides the actors in these cities (for (for example, cities) or when the connec- example, multinational firms, political lead- tions between some pairs of nodes are strong ers, cultural organisations, social movements) relative to other pairs. For example, in this with greater opportunities to strategise and network, the bandwidth connection between innovate. In addition, however, recursive New York and London is 96 599 Mbps while power indicates that these cities also have high the connection between Manila and Jakarta bandwidth connections to cities that have is only 10 Mbps. Using eigenvector-based few other high bandwidth connections. This measures in such cases, although technically position of power allows these cities to control possible, yields centrality and power scores the flow of information to certain parts of the that are equal or nearly equal to each other network because they act as the sole gateways and to ordinary degree centrality. As a result, through which some cities gain access to the they offer no additional information about global Internet backbone. By simultaneously network position. occupying a position of centrality and a Plotting the 82 cities by both their recur- position of power in the world city network, sive centrality and recursive power in this cities like London and New York capture the network, Figure 3 illustrates that centrality structural advantages of both resource accu- and power are distinct characteristics of mulation/diffusion and resource control, and cities’ network positions. This suggests that thus stand apart as quintessential world cities. positional status in the world city network is However, positions of centrality and power not a unidimensional phenomenon ranging are not always found together. As Figure 3 from highly central and powerful world cities illustrates, a second group of cities—Paris, to peripheral and powerless lower-tier cities. Amsterdam, Washington, Brussels and Instead, network status is better understood Chicago—occupy highly central positions in as a multidimensional phenomenon where the network, but do not occupy positions that centrality and power are independent and afford them significant amounts of power. By combine in various ways to constitute distinct occupying highly central positions, these cities types of world cities (see Guimera et al., 2005). are likely to be resource rich, with structural The most obvious examples of world opportunities to accumulate and diffuse the cities—London and New York—lie at one commodities that flow through the network extreme. Indicated by their position in the (in this case, information). They are not, upper-right corner of Figure 3, these cities however, likely to have much influence over occupy positions in the Internet backbone the flow of those resources elsewhere in the network that make them both highly central system and thus little ability to control the
2744 ZACHARY NEAL
Figure 3. Comparing recursive centrality and power in the Internet backbone network.
activities in other cities. Quite different from resource concentrations or particularly effective
the quintessential world cities of London and at diffusing resources through the network.
New York, these ‘central but not powerful’ Quite different from both quintessential and
places are a unique type of world city char- hub world cities, these ‘powerful but not
acterised by their role as hubs. Such places are central’ places are characterised by their role
likely sites of innovation because they benefit as gateways. Such places are likely to be sites of
from the high concentrations of capital and instrumental and co-ordinative activities (for
the ability to disseminate new information example, banking, advertising and consulting)
that is necessary for such activities. In this that facilitate the more primary activities found
case, the role of hubs as centres of national in hub world cities. In this case, because the
(for example, Paris, Washington) and trans- Internet backbone network is constituted by
national (for example, Brussels) government physical infrastructure, the most powerful cities
also highlights the ability of cities in central are located at the geographical edges, serving as
positions efficiently to communicate policy the principal entry points for their respective
and diplomatic messages to wide audiences. continents. However, in other less physically
A third group of cities—Miami, Stockholm, grounded networks such as the branch office
San Francisco, Los Angeles and Tokyo—are networks of advanced producer service firms,
the mirror image of hubs, occupying positions the spatial organisation of powerful gateway cit-
of power but not of centrality. By occupying ies and central hub cities may be less patterned.
positions of power, these cities are likely to
be highly influential, with structural oppor-
Discussion and Conclusion
tunities to function as gatekeepers that can
mediate or broker other cities’ access to the By examining both hypothetical and observed
resources flowing through the network. They world city networks, these analyses sug-
are not, however, likely to be sites of significant gest that centrality and power are distinctDIFFERENTIATING CENTRALITY AND POWER 2745 characteristics of world cities that derive classifications of cities that have focused on from distinct structural patterns of linkages. combinations of city attributes (for example, Occupying a position of centrality in the Boschken, 2008) because it links cities’ roles world city network does not automatically directly to the structural properties of the translate into structural opportunities to world city network. This is a major strength exercise power. To differentiate effectively because it paves the way for future studies positions of centrality from positions of to examine how the structurally defined power requires moving beyond relatively roles of quintessential, hub and gateway city simple measures such as degree centrality. In are associated with such attributes as firm addition, empirical analysis of the world city location or demographic diversity without network requires accounting for the differing undue circularity. strength of intercity linkages, which limits Conceptualising centrality and power in the the usefulness of closeness and betweenness proposed recursive manner, where a city’s sta- measures, and attending to the mathemati- tus depends not only on its own connections cal properties of highly sophisticated net- but also on the connectivity its contacts, also work indices, which limits the usefulness of has implications for understanding changes eigenvector-based measures. The proposed in the structure of the world city network. A measures of recursive centrality and recursive given city’s status in the global arena depends power offer a practical solution to these issues. in part on the number and strength of exter- These measures effectively differentiate cen- nal linkages it maintains. However, equally trality from power in theoretically informed important are the number and strength of ways, are computationally simple and can external linkages maintained by those cities be applied to networks where some linkages to which it is connected. Thus, whether a vary in strength. city’s status rises or falls over time depends More than simply a methodological inno- not on its own internal features, nor on its vation, however, these analyses have chal- own network, but on the structure of the lenged the conception of world cities’ status entire world city network. This more global in networks as a unidimensional, hierarchi- understanding of world city status suggests cal phenomenon. Rather, they suggest that that purposive attempts to enhance a city’s positional status in the world city network global status may be quite difficult and, is a multidimensional phenomenon that has indeed, may lie outside the reach of a city’s implications for the roles that cities play in the own leaders. Nonetheless, for cities seeking a world system. First, quintessential world cities more global identity, urban leaders must look simultaneously occupy positions of centrality beyond simply forging newer and stronger and power, and serve as the principal outposts external linkages, and focus on forging stra- of economic, political and social globalisation. tegic linkages. Enhancing resource concentra- Secondly, hub world cities occupy positions of tion potential (i.e. centrality) requires new centrality but not power, and serve as sites for connections to well connected places, while resource concentration and diffusion where enhancing command-and-control potential innovation and investment activities are sup- (i.e. power) requires new connections to ported. Finally, gateway world cities occupy poorly connected places. positions of power but not centrality, and serve Yet, just as centrality and power may occur as gatekeepers that gain influence through independently, they are also likely to occur in their ability to broker and mediate other cities’ different combinations based on the substance access to the rest of the network. This typol- of the network in question. In the analysis ogy differs from previous multidimensional presented earlier, the most powerful cities
2746 ZACHARY NEAL
were those located at the edges of continents, Notes
because they were geographically convenient
1. Any discussion of urban systems risks
gateways for the Internet’s physical infra-
reifying cities and treating them as actors.
structure. However, examining other types The variety of forms that urban networks
of network that map the flow of different may take yields an equal variety of actors
resources (for example, foreign direct invest- that constitute and maintain the networks.
ment, migration) would be likely to reveal that In intercity transport and communication
the same cities play unique roles in other con- networks, individuals (such as passengers,
texts. The two earlier analyses illustrate one callers) are the true actors. In command-
such case: Paris is powerful but not central in and-control networks like those discussed
Friedmann’s economically focused network, by Alderson and Beckfield (2004), firms
(given agency by executives) are the actors.
yet it is central but not powerful in a commu-
Finally, in political networks like those forged
nication infrastructure network. Thus, cities by sister-city relationships, the cities (given
may play the role of a gateway world city in agency by political leaders) are the actors. For
some domains, while playing the role of a hub the sake of simplicity, cities are discussed as
world city in others. The character and status the actors responsible for the network, but it
of any given city in the global arena, therefore, is recognised that the actual actor depends
is the result of its varying levels of centrality on the type of network and the conceptual
and power in each of several networks. Indeed, level of analysis.
the two measures developed in this paper can 2. This paper aims to clarify methods of
be applied to world city networks defined to analysing world city networks, specifically
by developing more robust measurements
capture not only exchanges of an economic
of cities’ centrality and power based on their
nature, but also cultural, political and social positions within such networks. Derudder
flows. Future research should focus not only (2006) has noted a related need for clarity in the
on how centrality and power differ in eco- data used to define the networks themselves.
nomic contexts, but how they differ in these He argues that there are two broad empirical
other global city arenas as well. approaches, each of which implies a set of
Notions of centrality and power are ubiqui- (often unstated) theoretical assumptions: a
tous in discussions of cities’ positions within corporate organisation approach that focuses
world city networks. Frequently, these concepts on producer service firms or multinational
corporations and an infrastructure approach
are treated as indistinct and are measured
that focuses on the built structures that
using conceptually simple or methodological facilitate communication and transport.
inappropriate instruments. However, centrality Although this paper and Derudder’s tackle
and power are conceptually distinct and have different issues, together they highlight that
unique consequences for cities, and therefore empirical world city research could benefit
should be differentiated in empirical investi- from more careful attention to issues of both
gations of world city networks. The proposed data and their analysis.
measures of recursive centrality and recursive 3. Notably, Alderson and Beckfield (2004)
power offer a promising approach that provides analysed a network of directed relationships,
a more refined and theoretically informed view which permitted the computation of two
types of degree centrality: in-degree centrality,
of cities’ network positions, while also over-
which counts the number of inbound linkages,
coming some of the methodological limitations and out-degree centrality, which counts the
of existing approaches. Together, they more number of outbound linkages. Although
accurately capture the multidimensionality of in- and out-degree centrality are distinct
world city status where cities play different roles measures, they are nonetheless still both
within and across different types of network. measures of centrality, and not of power.DIFFERENTIATING CENTRALITY AND POWER 2747
4. Eigenvector centrality is a measure of centrality Boschken, H. L. (2008) A multiple-perspectives
only. In contrast, the operation of beta construct of the American global city, Urban
centrality, which is also sometimes called Studies, 45, pp. 3–28.
Bonacich Power, depends on the value of the Bourdieu, P. (1986) The forms of capital, in: J.
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b > 0) or power (when b < 0). pp. 241–258. New York: Greenwood.
Castells, M. (1996) The Rise of the Network Society.
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Acknowledgements Choi, J. H., Barnett, G. A. and Chon, B. (2006)
Comparing world city networks: a network
The author would like to thank Junho Choi, George analysis of internet backbone and air trans-
Barnett, and Bum-Soo Chon for kindly providing port intercity linkages, Global Networks, 6,
their data on the internet infrastructure network, pp. 81–99.
and Jennifer Watling Neal and Ken Frank for their Cook, K. S., Emerson, R. M., Gillmore, M. R. and
comments on earlier drafts. Tamagishi, T. (1983) The distribution of power
in exchange networks: theory and experimen-
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