GaWC Research Bulletin 143

This Research Bulletin has been published in American Journal of Sociology, 112 (3), (2006), 881-894.

doi:10.1086/510991

Please refer to the published version when quoting the paper.

(Z)

Parallel Paths to Understanding Global Inter-City Relations¹

P.J. Taylor

Abstract

This is a short comment comparing Alderson and Beckfield’s recent comprehensive study of world cities to parallel work carried out by the Globalization and World Cities (GaWC) Study Group and Network. It is shown that starting from the same stimulus – to overcome a key data deficiency - the two research projects use different network models, and thus different analyses producing distinctive results. Findings and interpretations are compared and assessed and it is concluded that while these reseaches are complementary to a degree, they still have important lessons to learn from each other.

INTRODUCTION

A recent paper by Alderson and Beckfield (2004) provides the most comprehensive empirical assessment of world cities that has so far been attempted. In this outstanding contribution to the literature on global inter-city relations, they analyse links between 3,692 cities based upon the organizational geographies of 446 of the largest multinational firms and their subsidiaries for the year 2000. Using network analysis techniques, new results on the ranking of cities and the structures of their inter-relations are produced that provide essential food for thought for all world city researchers. Thus Alderson and Beckfield stimulate us to rethink many commonly accepted but empirically uncorroborated ideas about world cities within the world economy.

The purpose of this comment is to compare and contrast Alderson and Beckfield’s project with a parallel empirical programme of world city research that is smaller in scope but still unusually large for this literature. The Globalization and World Cities (GaWC) Study Group and Network² has developed a project that analyses links between 315 cities based upon the organizational geographies of 100 global service firms (Derudder et al. 2003; Taylor 2001; 2004a; Taylor and Derudder 2004; Taylor and Walker 2004; Taylor et al. 2002a; 2002b; 2002c; 2004). There are striking similarities in the approaches of these two research efforts but there are also very distinctive and important differences in the modelling and analyses, and hence results. What is, perhaps, remarkable is the fact that the projects have progressed in parallel with little or no reference to each other.³ This short paper is a first step towards rectifying this unfortunate situation.

These particular ‘parallel paths’ repeat a long-term tendency in the study of inter-city relations for research to occur within separate disciplinary traditions, with intermittent contacts. There is a geography/planning tradition (Christaller-Dickinson-Berry) that deals with settlement patterns and typically treats cities and towns as different levels of service center. The parallel sociology tradition (McKenzie-Hawley-Duncan) deals with the relative power of cities and typically treats cities in terms of their metropolitan dominance. Of course, there have been important interactions between these two types of urban study but they have tended to remain relatively distinctive. The research pedigrees of the two most cited world city researchers, John Friedmann and Saskia Sassen, are from geography/planning and sociology respectively. However, it might be expected that with this new scale of analysis, in what are often seen as increasingly post-disciplinary times, such a research division should be in the process of dissipating; this paper is intended to help this process along.

The discussion is presented in four sections. First, I begin by setting out the common starting point of Alderson and Beckfield’s study and the GaWC research. Both researches identify the same problem and they devise quite similar solutions. Second, the first divergence comes with the choice of network model: social network analysis in contrast to an interlocking network model. This inevitably leads to different forms of operational matrix for analysis. Third, these matrices are subjected to alternative analyses covering both city rankings and network structures. Fourth, different results produce different interpretations of global inter-city relations. Complementarity between these divergent findings is sought. In all sections there is an attempt to provide an honest appraisal of the advantages and disadvantages of the two research efforts. The key advantage of each approach is identified in a short conclusion.

COMMON STARTING POINTS

It has become commonplace to bemoan the paucity of data when studying world cities (e.g. Short et al. 1996). However, both Alderson/Beckfield and the GaWC research take a particular take on this criticism emphasizing relations and that then leads on to a similar solution.

The data deficiency problem. The problem is not only that comparative data across cities worldwide is difficult to assemble, it is that what is collected are invariably attribute data. Such data are not necessarily very helpful for studying inter-city relations. For sure, cities can be ranked using attributes, such as population or size of stock exchange, but these do not measure inter-city relations. City ranking on its own does not specify an urban hierarchy despite this frequent assumption in the literature (Taylor 1997). Thus, without relational data between cities, the structure of global inter-city relations can only be ‘impressionistic’ (Alderson and Becksfield 2004, p. 812) resulting in serious ‘empirical blemishes’ in otherwise sophisticated urban studies (Taylor 2004a, pp. 32-6). Obtaining relational data means finding social measurements⁴ between pairs of cities; such official information is scarce within countries, at the transnational level it is simply absent.

The corporate organization solution. Current global inter-city relations are premised upon the combined computer and communication revolution that allows for instantaneous worldwide connections. It is multinational enterprises (MNEs) who have taken full advantage of this new technology to create what we now call economic globalization (Dicken 2003). Firms with ‘global reaches’ or transnational fields of activity have generated new city-centered geographies. Such firms’ activities are premised upon intra-firm communications between different parts of their holdings: Alderson and Beckfield (2004, pp. 813-4) consider this to be a ‘key relation’ in ‘an MNE-generated city system’; similarly, Taylor (2004, p. 59) argues that it is ‘firms through their office networks that have created the overall structure of the (world city) network’. Thus it follows that collecting data on the organizational geography of large MNEs will enable the inter-city relations of corporate activity to be estimated. Both the Alderson/Beckfield study and the GaWC research pursue this solution to the data deficiency problem.⁵

BASIC MODELLING DIFFERENCES

The first difference between the two research projects concerns the MNE’s that are studied. In the Alderson/Beckfield research the Fortune Global 500 largest MNEs are used, reduced to 446 to cope with data availability difficulties. In the GaWC research only ‘global service firms’ are used. Thus, whereas the Fortune 500 includes a wide range of economic sectors, the GaWC study uses only firms providing advanced producer services (the main overlap with the Fortune 500 is in banking/finance). This different selection of firms arises from the two studies adopting dissimilar models of global inter-city relations.

Global command centers and social network analysis. Following the lead of Smith and Timberlake (1993), the Alderson/Beckfield research attempts to match world city relations to social network analysis. For this process world cities are interpreted as command centers housing the headquarters of major MNEs (broadly following Friedmann 1986).⁶ Thus they collect data on the HQs of their 446 firms and all their subsidiary locations. From this they produce a directed (from HQ to subsidiary), valued (number of directions to and from a city) matrix linking 3,692 cities across the world (Alderson and Beckfield 2004, p. 813). With this matrix they are able to apply the ‘set of tools’ that have been developed in social network analyses to evaluate the positions and power of individuals in a network. Thus the positions and power of world cities within the ‘world city system’ can be measured and evaluated (Alderson and Beckfield 2004, pp. 812-3).

Global service centers and the interlocking network model. The GaWC research is premised upon a different conceptualisation of world cities drawn largely from Sassen (2001). This focuses upon the attraction of advanced producer service firms (providing professional, financial and creative services for businesses) to major cities with their knowledge-rich environments and specialist markets. In the 1980s and 1990s many such service firms followed their global clients to become important MNEs in their own right. They serviced their old clients and searched for new clients through creating worldwide office networks covering the major cities in most or all world regions. Thus it is argued that these firms ‘interlock’ world cities through their intra-firm communications of information, knowledge, plans, directions, advice, etc. to create a network of global service centers. Viewed in this way, a world city network can be formally specified as an interlocking network (Knoke and Kuklinski 1982, p. 60; Taylor 2001; Taylor 2004a, pp. 60-4). Such a network differs from the social network analysis Alderson and Beckfield employ in having three rather than just two layers: as well as the net level (world economy) and the nodal level (cities), there is a subnodal level of interlockers (the service firms). In this case, the initial matrix of interest is a ‘service values matrix’ that arrays cities against firms with service values indicating the importance of a given city to the office network of a given firm. In the GaWC research, service values for each firm are coded from 5 (headquarter city) through to 0 (indicating no presence in a city). Service values are based upon the size of offices and their extra-city functions (e.g. a regional office); the assumption is that the higher the service value the more communication flows are generated towards other cities (Taylor et al. 2002a; Taylor 2004a, pp. 65-7). Using this matrix, a statistical set of techniques has been employed to evaluate cities and the structure of their network (Taylor 2004a).⁷

Comparison. The first point to make is that the two modelling exercises can be seen as complementary, one measuring the command dimension of world cities, the other the business service dimension. However, there can be a debate about which is the more important for understanding global inter-city relations. Undoubtedly, the most impressive feature of the Alderson/Beckfield study is the sheer scale of evidence brought to bear on the inter-city relations. In addition, the model of controlling cities matches well with the current imagination of economic globalization, a sort of alternative to the tradition power politics of international relations. But herein lies its disadvantage. The theory of the firm underlying this model is a simple one of direction, from which is derived a hierarchy of cities. Using the service values in the interlocking model allows for a more subtle approach to relating cities to firms: with services there is often much more of a network organization than a simple hierarchy. But the major advantage of using an interlocking network is that it keeps the economic agency – the firms – to the fore. Firms are lost to the analysis in the creation of the city x city matrix for the social network analysis. This can lead to a reification of the city: for instance, with the idea that the analysis shows ‘prestigious cities’ ‘are sought out by other cities’ resulting in a ‘fair degree of deference in the world city system’ (Alderson and Beckfield 2004, pp. 824, 833). This may make sense for a network of individuals but it is problematic for cities. The interlocking network operates precisely to avoid this problem (Taylor 2004a, pp. 56-9). But the latter approach requires much more work to create much less data so that its finding will be inevitably less robust and reliable than Alderson and Beckfield’s results. In particular, there is great potential to produce a robust longitudinal study of cities in globalization using their command approach.

ALTERNATIVE ANALYSES

Different models means that the matrices to be analysed are different: a city x city matrix and a city x firm matrix. However both research projects employ similar techniques. There are two basic forms: the first generates rankings of cities in terms of different senses of importance; the second provides measures of the structure of the overall network.

Ways of ranking cities. Using the social network ‘toolkit’ Alderson and Beckfield (2004, pp. 822-4) employ four measures of network centrality: outdegree centrality, closeness centrality, betweenness centrality, and indegree centrality. The middle two measures are calculated after converting the asymmetric valued matrix into a simple symmetric, dichotomous matrix; this makes them inherently less interesting for understanding inter-city relations and I will not consider them further here. This leaves outdegree and indegree, which are measured as the number of ties sent and ties received respectively. Hence outdegree centrality measures cities with firm HQs and is the sum of the ‘branches’ controlled from those HQs. Alderson and Beckfield (2004, p. 822) interpret this as a direct measure of the power of a city. In contrast, indegree centrality is the sum of branches in a city. Alderson and Beckfield (2004, p. 824) interpret this as the prominence or prestige of a city - ‘places chosen over others’. In the interlocking model there is one basic way of assessing a city’s importance within the network: its total interlock connectivity (Taylor 2001; 2004, p. 68-70; Taylor et al. 2002a). For each city, this involves summing the products of every firm’s service value in the city with their service values in all other cities. This is termed the ‘global network connectivity’ of a city as defined by global service firms operating as interlockers. This provides an overall measure of the importance of a city within the network. Such a measure can be disaggregated to consider just dominant links (where a city’s service values are larger than another city) or just subordinate links (where a city’s service values are smaller than another city). Such measures of dominant and subordinate connectivity are clearly similar to outdegree and indegree measures of centrality respectively. In this case they are interpreted as measuring dominant centers and gateway cities respectively (Taylor et al. 2002c; Taylor 2004a, pp. 88-9, 93).

Ways of detecting configurations in networks. The standard technique for social network analysis is blockmodeling which assigns individuals to sets on the basis of their inter-relations. In Alderson and Beckfield’s (2004, pp. 824-7) analysis this means grouping cities together in terms of similarities in their ties to other cities. In this way the generalised structure of the network is uncovered. In contrast, the initial technique applied to the city x firm data for the interlocking model is a simple principal components analysis wherein either cities (Q-mode analysis) or firms (R-mode analysis) are clustered using their correlations to define the ‘principal components’ of the data (Taylor et al. 2002b; 2004; Taylor 2004a, pp. 129-65). These define common patterns of service profiles among cities or common patterns of locational strategies among firms. This provides a parsimonious description of the structure of the interlocking network. A more sophisticated technique is fuzzy set analysis which has been used to classify cities, again in terms of similarities in services offered, but wherein overlapping groupings are explicitly allowed (Derudder et al., 2003; Taylor 2004a, pp. 165-75; Taylor and Derudder 2004). This can produce quite a complex patterning of cities.

Comparison. Neither research project claims to be innovative in its analyses: one employs the usual techniques of network analysis, the other simple connectivity measures and common statistical techniques for data reduction/classification. It is interesting that they are both trying to measure and delineate similar features of cities and networks. The proof of the pudding is in the results, of which more below. One important advantage of the formal network analyses is that the configuration of blocks are characterised specifically in relations between and within blocks. Furthermore, the blocks are used to carry out a rigorous test of whether general core-periphery patterns are being reinforced or undermined by the rise of world cities (Alderson and Beckfield 2004, pp. 841-6). With the principal components analysis and fuzzy analyses, these questions are only addressed discursively (Taylor 2004a, 197-200). But by starting with the city x firms matrix, the techniques used for the interlocking model produce results in which both cities and firms appear which makes for interpretation of results in which the economic agency remains overt.

DIFFERENT RESULTS AND INTERPRETATIONS

Although searching for similar features of cities and their networks, the different models and analyses will inevitably produce dissimilar results and thus provide for alternative interpretations.

Different rankings of world cities. For initial discussion I have identified the top 10 ranked cities for each of the various measures of city importance reviewed above (Table 1). The first thing to note is that outdegree and indegree measures create overlapping lists in Table 1 – five cities appear in both lists. There are important differences in the ranking of these five, notable with Tokyo ranked top as a headquarter city but only 4th for indegree centrality. But the interesting feature are the two sets of five cities that are found in just one list: Düsseldorf, Zurich, Munich, Osaka and San Francisco as headquarter cities, and Los Angeles, Chicago, Brussels, Singapore and Hong Kong for indegree centrality. Clearly the first five are major centers of either industry or banking which accounts for their inclusion as headquarter cities. The second group are harder to interpret. Alderson and Beckwith (2004, p. 834) suggest that they indicate ‘prestigious cities’ but, as I have indicated earlier, I think this particular transferring of social network thinking to city networks is unhelpful: I will have more to say on this in the discussion of interpretations below. For the interlocking model, the global network connectivity list overlaps with both outdegree and indegree centrality lists, it appears as a sort of ‘mixed list’. Why mixed – Hong Kong, Singapore, Chicago and Los Angeles as well as the ‘big four’ – London, New York, Paris and Tokyo? Because this measure of connectivity encompasses all links in the data and so provides an overall picture of the location of a city in the network. The dominant city list is very similar to the latter list but there are important variations: Frankfurt and Amsterdam replacing Milan and Madrid. The former pair, as important financial centers, have more domination links in business services than their southern European neighbors. Finally, the subordinate connectivity list provides a largely new set of cities; only Zurich and Brussels have appeared on a previous list. These are cities with few major offices, but they attract most global service firms who locate ‘ordinary’ offices there. In other words these are places where it is necessary to be for a global location strategy to provide business services. The eight cities unique to this list are prime gateways into important developing markets. Brussels and Zurich are different sorts of ‘places to be’, they are particular gateways into European political action and financial action respectively.

Comparing interpretations of rankings. Clearly differences between the two sets of world city rankings in Table 1 result from the different universes of firms used. For instance, Tokyo leading the outdegree list which also includes Osaka represents a general Japanese economic prowess that is somewhat diluted when the focus turns to just service firms. In fact, one of the intriguing features of the global and dominant connectivity lists is the ranking of Hong Kong above Tokyo and, in the process, splitting the ‘big four’ in the social network analysis in two. For business servicing, it seems that Hong Kong, where advanced business knowledge (financial, professional, creative) intersects with strategic geographical knowledge (Chinese economic, political and cultural information) to create a key center of market opportunity, is a place where any firm aspiring to provide a global service for its clients just has to be. Such centers are undervalued in the Alderson/Beckfield study because they have only a two-stage level of information (HQ/subsidiary). Their work misses out regional headquarters that are common in cities such as Hong Kong and Miami. The latter is not in the top 50 for outdegree centrality but ranks 15th in the GaWC dominant connectivity list because it houses numerous ‘Latin American regional HQs’ (Taylor et al. 2002c). In general, as Godfrey and Zhou (1999) have noted, using data on HQs to delineate world cities creates a ‘North bias’ in ranking. This is counter to Alderson and Beckfield’s (2004, p. 828) statement that ‘outdegree is an unambiguous indicator of world city-ness’. In fact, headquarter functions are not becoming more concentrated in world cities (Salmon and Lyons 1995); they tend to be located in the origin city of a firm, and the city may well not have grown in importance at the same rate as the firm. This shows that headquarter functions do not have to be carried out in major world cities, although important presence in the latter is normally found to be necessary. Thus Vevey ranks 12th for outdegree centrality (it is a small town near Lucerne in Switzerland) just ahead of Chicago on 13th: is the former really more of a world city than the latter? Alderson and Beckfield (2004, p. 834) ask this same question with respect to Omaha, Peoria and Rochester being more powerful than ‘cities such as Barcelona, Miami, Vancouver, Johannesburg, Jakarta, Prague, and Shanghai’. This is in the context of their discussion of indegree centrality indicating the prestige of a city. They go on to argue that ‘there may be a tendency in the literature on world cities to mistake prestige for power’. But there is an alternative interpretation: power does not have to be limited to ‘power as capacity’ or domination, there is also ‘power as a medium – a “networked” conception’ (Allen 1997, p. 70). The latter involves not the ability to command but is about position in the network, strategic places where it is necessary to be. This is, of course, how the GaWC project interprets Hong Kong, Miami and the list of cities with subordinate links in Table 1. Hence, I would replace the concept of ‘prestige’ in Alderson and Beckfield’s interpretation with the idea of network power – places to be for good strategic reasons. Hence, Barcelona (ranked 32nd for global network connectivity) is more ‘powerful’ than Omaha (ranked 223rd) in the world city network.

Alternative configurations of the networks. Alderson and Beckfield’s (2004, pp. 835-7) blockmodeling allocated their 3692 cities to 53 classes or blocks, 17 of which were singletons leaving 34 blocks for study. These are identified as 4 basic types. First, primary blocks are groups of cities that are very ‘active’; they have high outdegree, indegree and intra-block links (cliquishness). There are seven such blocks including the paramount block comprising London, New York, Paris and Tokyo: it sends 37% of all ties, it receives 15%, and 23% of its ties are intra-block (Alderson and Beckfield 2004, p. 835). Second, there are five cliques with high levels of intra-block ties. Third, five other blocks are defined as ‘snobs’ characterised by just indegree. The rest are isolate blocks that are deemed to ‘constitute the periphery of the city system’ (Alderson and Beckfield 2004, p. 837). In further analyses, Alderson and Beckfield (2004, pp. 841-6) show that these categories statistically fit the world-systems tripartite division (core, semi-periphery, periphery). Configurations of the interlocking network of service centers produces a similar patterning but with more specific geographical labelling. For instance, in the Q-mode principal components analysis the primary structure is a 5-cluster solution that produces US, European, Pacific Asian, ‘old’ Commonwealth, and ‘Outer’ groups of cities (Taylor et al. 2002b; Taylor 2004a, pp 150-4). The latter is interpreted as ‘periphery’ but it is not clear whether it corresponds to the isolate blocks since these cities are not fully listed by Alderson and Beckfield (2004, Table 5). These analyses also show regional/sectoral patterns, for instance the dominance of banking/finance firms in the constitution of the Pacific Asian service region (Taylor et al. 2002b, 2004; Taylor 2004a). However, in many ways the fuzzy set analyses are much more like the Alderson and Beckfield’s results. A total of 22 global urban arenas are identified, and found to be differentiated by connectivity level and region (Derudder et al. 2003; Taylor 2004a, pp. 166-74; Taylor and Derudder 2004)). At the apex of the world city network there are four arenas that bear some resemblance to Alderson and Beckfield’s primary blocks. London and New York are the paramount arena (with just services these two far outstrip Paris and Tokyo) and there are three other central arenas bringing together international financial centres (Frankfurt, Hong Kong, Paris, Singapore, Tokyo), leading US cities (Chicago, Los Angeles, San Francisco), and a European-linked grouping (Amsterdam, Buenos Aires, Madrid, Mexico City, Milan, Sao Paulo, Sydney, Toronto, Zurich). These can be interpreted as defining the ‘major routes’ in the global space of service flows (Taylor and Derudder 2004).

Comparing the configurations. As well as the differences in approach previously highlighted, there are two dissimilaries between the social network and interlocking network models that are particularly pertinent for comparing the analyses. First, there is the matter of a tenfold difference in number of cities studied: the GaWC project’s roster of 315 cities is large but is totally dwarfed by Alderson and Beckfield’s 3692 cities. This means that comparison is really only sensible for the higher strata of world cities: as shown above these appear reasonably consistent. Second, the interlocking model analyses have featured geographical pattern (regionalism) at the fore of their concerns whereas Alderson and Beckfield employ only a general core-periphery spatial pattern. This obviously relates back to the disciplinary traditions from which the two research projects derive. However, there are two features where we can find each approach producing important findings not replicated by the other. First, the blockmodeling locates groups of cities within the network in terms of the nature of their ties. This goes beyond city classification, it directly informs the position and role of cities within the network. Clearly such findings are of fundamental importance to understanding global inter-city relations. Second, the principal components models keep both cities and firms in play so that the agency of world city network formation remains to the fore. Thus, equally clearly, these findings are also of fundamental importance to understanding global inter-city relations. Put simply, each research project has key analytical insights to learn from the other.

CONCLUDING COMMENTS

The basic conclusion is that these two parallel projects will benefit from some cross-disciplinary fertilization at a variety of levels. Thus, although we can search out similarities and argue that the researches are complementary, this is not enough. There are two distinct elements that are largely monopolised by just one of the projects that the other needs to seriously address. First, the size of the Alderson and Beckfield study has been referred to often above but needs further emphasis as the critical feature of their work. This is truly a study of the world economy in the whole: Fortune's Global 500 had combined revenue of $12.6 trillion in 2000 and thus they account for ‘a notable proportion of total world economic activity’ (Alderson and Beckfield 2004, p. 820). Hence, this project locates cities at the heart of economic globalization. The GaWC project’s focus on services is justified as measuring ‘cutting-edge’ economic activity within globalization, but it deals with only a small section of the world economy: beyond the banks, only one other service firm appears in Alderson and Beckfield list of firms (in advertising). Thus, it is to Alderson and Beckfield that we must refer to understand the contemporary city-centred world economy. Second, the GaWC approach’s focus on services does, however, provide it with its own defining advantage: it links the study of global inter-city relations to questions about the nature of cities. In particular, it is presented as a contemporary expression of Jacobs’ (1984) seminal work on the nature of city economies within a space-economy (Taylor 2004a, pp. 42-51). Cities are not just entrepôts in the flows of commodities, they are the dynamic creative centers of the wider economy: today world cities are the dynamic centers of economic globalization. Alderson and Beckfield’s focus upon control does capture an important dimension of this globalization, and is in keeping with the research tradition from which they come, but it leaves their study with a limited notion of world city-ness.

Finally, there is one important point that both projects agree upon. To understand global inter-city relations it is necessary to consider more than just economic processes. Alderson and Beckfield (2004, p. 848) conclude with a call for research on ‘more culturally, socially, and politically informed senses of the power of cities’ and are extending their work in this direction (Alderson and Beckfield 2002). Similarly the GaWC approach is being applied to other cultural, social and political world city network makers in work on comparative connectivities and articulator cities (Taylor 2004ab). This is a rich vein of important research that both projects can contribute to, but hopefully not along parallel and separate paths.

REFERENCES

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Alderson, Arthur S. and Jason Beckfield. 2002. "Globalization and the Centralization of power in the World City System." Paper presented at the XVI World Congress of Sociology, Brisbane, Australia, July

Castells, M. 1996. The Rise of Network Society, Oxford: Blackwell

Alderson, Arthur S. and Jason Beckfield. 2004. "Power and Position in the World City System." American Journal of Sociology 109: 811-51.

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NOTES

1. The research has been supported by the Economic and Social Research Council (UK). Direct all correspondence to Peter J. Taylor, Department of Geography, Loughborough University, Loughborough, LE11 3TU, UK. E-mail: p.j.taylor@lboro.ac.uk.

2. This is a virtual research center: www.lboro.ac.uk/gawc.

3. Alderson and Beckfield do refer to two early GaWC papers but they are before the development of the interlocking model discussed here.

4. I use the phrase ‘social measurements’ to indicate evidence concerning the agents that are creating the world city network through carrying out their routine business. Here I am thinking of the second layer of Castells’ (1996) ‘space of flows’ in contrast to the first layer that is the infrastructure which enables his ‘network society’ to function. Included in the latter are airline networks that have been used to describe the world city network (Smith and Timberlake 1993). Such measures have their own problems but, as infrastructure networks, they are not part of my subject matter here.

5. Note that this solution can only provide indirect estimates of network connections since there is no actual evidence for quantity of intra-firms flows. For reasons of both confidentiality and size of task, it is highly unlikely that such evidence will ever be available in sufficient quantities to provide for an overall picture of the world city network - thus the need to produce indirect measures.

6. It can be noted that this source appears to come from the 'wrong' side of the tradition divide identified earlier. However, Friedmann's interest in the power of cities is very exceptional in the geography/planning literature (Taylor, 2004a, p. 87).

7. The GaWC research has experimented with standard network techniques (e.g. Derudder and Taylor 2003; Taylor 2004a, pp. 113-21) but no where near as extensively as Alderson and Beckfield. The former are not discussed here.

Table 1: Alternative Top 10 Rankings of World Cities

Sources: Alderson and Beckfield (2004, Table 3); Taylor et al . (2002c)

Edited and posted on the web on 26th April 2004; last update 23rd March 2005