GaWC Research Bulletin 383

This Research Bulletin has been published in Geographical Analysis, 44 (2), (2012), 171-173.

doi:10.1111/j.1538-4632.2012.00844.x

Please refer to the published version when quoting the paper.

(Z)

Two-mode Networks and the Interlocking World City Network Model: A Reply to Neal

X. Liu^* and B. Derudder^**

Abstract

We present an alternative perspective on Neal’s (2011) critique of Taylor’s (2001) specification of the world city network. To this end, we discuss Taylor’s Interlocking World City Network (IWCN) approach in terms of two-mode social networks, and use this discussion to evaluate Neal's ‘five structurally determined features’ of the IWCN model. The paper is concluded by reviewing the implications for quantitative WCN research based on the IWCN model.

Introduction

In a recent paper published in Geographical Analysis, Neal (2011) presents a critical discussion of Taylor’s (2001) interlocking world city network (IWCN) model. He thereby argues that the operationalization of the IWCN model with 315 cities and 100 firms is structurally pre-determined, reveals some practical implications of this ‘structural determinism’, and points to some alternatives. Neal’s critical reading of the IWCN model is refreshing and even path-breaking in the sense that it is – to the best of our knowledge – the first rigorous assessment of the basic tenets of this model¹. Indeed, a critical review of the assumptions underlying the IWCN model has long been overdue given that this model has been widely adopted in WCN research², e.g.:

• The IWCN model has been used as a starting point for empirical analyses of the WCN by applying it to data on the location strategies of a selection of transnationally organized producer services firms (e.g. Taylor et al., 2002; Taylor et al., 2011);

• Its conceptual underpinnings have been further contextualized, detailed and refined (e.g. Beaverstock et al., 2002; Derudder, 2006);

• The IWCN approach has been applied at other scales, especially in the context of the analysis of polycentric city-regions (e.g. Pain, 2008; Hoyler et al., 2008);

• The geographies of other transnationally organized agent have been analyzed through the lens of the IWCN model, including media firms and Islamic financial services firms (e.g. Watson et al., 2009; Bassens et al., 2010).

In this paper, we present an alternative perspective on Neal’s critique of Taylor’s model. The gist of our line of argument is that although Neal’s critique raises some thought-provoking points of attention, it tends to conflate problems associated with the analysis of two-mode networks with problems associated with the IWCN model per se. This conflation is crucial in that it puts some of the alleged flaws of Taylor’s model in a different (and less damning) context that furthermore allows for other solutions to be devised.

We begin with a brief introduction to two-mode networks and the position of Taylor’s IWCN approach in this regard, and discuss some of the implications for the quantitative analysis of WCNs. We then consecutively review our take on Neal's ‘five structurally determined features’ of the IWCN model, and conclude by reviewing the implications for quantitative WCN research based on the IWCN model.

Two-mode networks and the world city network

Data used in social network analysis (SNA) most commonly measures relations at the individual level, after which SNA techniques are used to infer the presence of social structures.  One straightforward example would be using data on ties between individuals in a community to infer the existence of coherent sub-networks (i.e. cliques) within that community.

However, many social networks are rather more complicated than this. Take, for instance, what has now become a classic study of the American South by Davis et al. (1941). To analyze both social ties and social events in a community, Davis et al. collected data on the presence of 18 women at 14 events of the ‘social season’.  By assessing patterns of presence at social events, it becomes possible to infer an underlying pattern of social ties, factions, and groupings among the 18 women. At the same time, however, by examining which women were present at the 14 events, it also becomes possible to infer underlying patterns in the similarity of the events (see Hanneman and Riddle 2005). The key point here is that this set of network data is different in that linkages identified in this study run between actors (the women) and structures (the parties of the social season): the network described here consists of ties running between two sets of nodes at two different levels of analysis, and there are no ties within the same set of nodes. Datasets like these involve two levels of analysis or ‘two modes’, resulting in some interesting analytic possibilities for gaining greater understanding of social structure.  In the Davis et al. study, for instance, it can be observed how the choices of individual women ‘make’ the meaning of the parties by choosing to attend or not; at the same time, it is also possible to see how the parties as structures may affect the choices of the individual women.

In conceptual terms, a two-mode or bipartite network thus consists of two disjoint sets of nodes (e.g., women and parties), whereby the primary data features links connecting nodes of the different sets (e.g., the presence of women at parties). And in principle, two one-mode networks (linkages between parties and linkages between women) can be projected from the two-mode dataset (linkages between women and parties). The concrete projection function can take different forms and can be used for very different purposes. In some cases, two-mode networks are explicitly collected as an intermediary step to be collapsed into a single one-mode dataset (Borgatti and Everett 1997). In an analysis of scientific collaboration, for instance, information is gathered on a two-mode network of authors and papers (author-by-paper); however, when the interest primarily lies in author collaborations (author-to-author), the alternative paper-to-paper one-mode network is often ignored (Newman et al. 2001). In other cases, without a sound conceptual motive for concentrating on one type of node, the duality of two-mode networks suggests no reason to favour either one-mode network (Breiger and Pattison 1986; Borgatti and Everett 1997).

For the purpose of the present research note, the key point is that Taylor’s (2001) IWCN model clearly represents a two-mode network consisting of two disjoint sets of nodes (cities and firms), whereby the primary data consists of links connecting nodes of the different sets (the presence of firms in cities). Based on this information on city/firm relations, it is in principle possible to obtain city-to-city and firm-to-firm one-mode networks (see Neal, 2008, for a practical example in the WCN context). Both types of one-mode networks are indeed examined in the economic geography and regional studies literature. For instance, research on urban systems focuses on cities as interlocked by infrastructure and multi-locational firms (e.g. Michelson and Wheeler, 1994; Taylor, 2001), while research on regional clustering focuses on the inter-firm networks formed by co-location of firms in cities or regions (e.g. Polenske 2004; Huber 2011)³.

Suggested readings for an overview of SNA techniques fit for analysing two-mode networks include the excellent introductory overviews by Borgatti and Everett (1997) and Latapy et al. (2008). In the remainder of this paper, we combine insights from this literature on two-mode networks with on-going quantitative research on WCNs to reframe Neal’s critical reading of Taylor’s IWCN model.

Structurally determined basic network structures

The first two structurally determined features of the IWCN identified in Neal (2011) are his observation that (1) the resulting WCN cannot have a ring structure if the number of cities (Ncity) is greater than or equal to the number of firms (Nfirm); and (2) that the resulting WCN cannot have a star or chain structure if the number of cities minus one (Ncity-1) is greater than or equal to the number of firms (Nfirm).

Although both observations are obviously correct, as a critique of the IWCN model these remarks are also somewhat superficial. Neal's necessary conditions for ring, star, and chain network structures are only discussed at the aggregate level (i.e. the WCN as a whole). However, the data used in the model does allow for these structures to be incorporated at ‘lower levels’. For instance, with 100 firms it is possible to have individual ring, star, and chain structures formed by as many as 99 cities.

Put differently: although it is accurate to state that the initial dataset used by Taylor (315 cities x 100 firms) cannot produce an overall WCN with a global ring/star/chain structure, it is incorrect to state that the dataset cannot reveal such networks within the WCN at large as the data is able to produce such ideal-typical structures in sub-networks. It is hereby useful to point out that there seems to be a consensus amongst WCN researchers that the WCN is in practice a combination of various local, regional and transnational urban networks with very different structures (see Castells, 2001)⁴. As consequence, it should not come as a surprise that all quantitative analyses of the WCN, although drawing on very diverse datasets and methodologies, reveal the existence of multi-layered and geographically very complex networks that bear no resemblance whatsoever to these ideal-typical structures.

Having thus recast Neal’s critique into the observation that the aggregate pattern of the WCN at large cannot assume a ring, star, or chain structures of 315 cities, the question becomes whether it is really that important to have the theoretical possibility of a ring/chain/star structure consisting of all 315 cities under investigation? In our reading, the answer is definitely negative, which implies that both structurally determined features are in practice not that pertinent. Moreover, Neal’s recommendation for including more firms than cities might not be useful due to the duality of the WCN. As discussed previously, we are interested in both one-mode projections of the WCN: city-to-city and firm-to-firm networks (Neal 2008). This implies that one would always find this so-called structural determinism in one of the one-mode projections in case of an unequal number of firms and cities.

Structurally determined cliques

The next two structurally determined features of the IWCN identified in Neal (2011) focus on cliques (i.e. coherent sub-networks) in the WCN: (3) the WCN cannot contain more than Nfirm cliques; and (4) the smallest clique contains at least Fmin cities, where Fmin denotes the number of cities that the smallest firm maintains an office in. Although both critiques are correct for the WCN generated by the IWCN model, it is important to point out that this is a general feature of one-mode projections of two-mode networks in general rather than a specific problem of the IWCN model.

From this perspective, the problem of the upper limit of the number of cliques can be reduced to the issue of the number of firms to be included in the dataset. This has been dealt with in the previous section, and we therefore confine ourselves to the structurally determined feature of the smallest possible clique. In principle, this problem can be tackled by deliberately introducing ‘small firms’ into the dataset or devising a randomised process to maintain the possibility of having small firms with the overall aim to achieve smaller cliques. In our view, however, this is not very useful empirical move as it runs counter to the theoretical underpinnings of WCN research in which it is argued that world cities primarily gain their power by being connected in the networks of large multinational enterprises (see also Alderson and Beckfield, 2004; Wall, 2009). In other words: there are good, theory-driven reasons for focusing on firms with sizable coverage and prowess (however defined). As a consequence, although we can counter the structurally determined feature of the smallest clique by introducing firms with presence in only three cities (the smallest possible size of a clique), this would be anathema to the entire idea of how the WCN is being structured in space.

Having said this, Neals’ point about the problem of the smallest possible clique is useful as it does suggest that IWCN researchers should remove firm inclusion criteria focusing on the minimal number of offices in different cities (e.g., 15 cities in Taylor et al., 2002). Rather, the focus should be on selecting the largest firms in sectors under investigation, which has been conventional in studies of city-firm relations (Alderson and Beckfield 2004; Taylor et al. 2011; Wall 2009). By removing this constraint on firm size, IWCN's inclusion criteria will contain less subjectivity, and let the smallest firm among these top firms  (i.e. a ‘population characteristics’ as Neal puts it) rather than researchers’ idiosyncratic choices determine the size of the smallest clique.

Structurally determined network density

The fifth and final structurally determined feature of the IWCN model identified in Neal (2011) is that ‘the size of the largest firm in the firm location matrix (...) constrains the density of the derived network.’ Again, this is a problem associated with projections of two-mode networks rather than a specific problem with the IWCN model, and can potentially be tackled by employing appropriate methodologies.

In the SNA literature, two major critiques of projections of two-mode networks into one-mode networks can be observed (Newman et al. 2001; Latapy et al. 2008): (1) information loss due to compression of the two-mode network; and (2) an inflation of linkages due to the inclusion of every possible pairwise link. The way in which these problems can be tackled are therefore logically in line with Neal’s (2011) proposed remedies: (1) rescale the network density and connectivity to allow for theoretical boundaries; and (2) adopt methods developed explicitly for analysing two-mode networks. As a consequence, we totally agree with Neal on this point, but we would add that more careful designs and interpretations of the projection function could be devised to reduce information loss and control linkage inflation when converting two-mode city-by-firm data into one-mode city-to-city data (Zhou et al. 2007; Barber 2007). Furthermore, as earlier discussed, adopting SNA techniques examining two-mode networks directly could prove to be very relevant, as both one-mode projections of the city-firm data may provide insights about an increasingly connected world (Castells 2001; Neal, 2008).

Conclusions

Neal’s (2011) paper takes the WCN literature an important step further in that it thoroughly discusses some of the basic assumptions of the IWCN model, thus revealing some structurally determined features in the network. In this short research note, we have reviewed Neal’s critiques and attempted to clarify the real implications of this so-called structural determinism. Based on our previous discussions, we arrive at following recommendations to be used alongside Neal’s:

1. It is indeed desirable to have more cities and firms in analysing city-firm relations. However, we believe it is not necessary to have more firms than cities for the following reasons: (1) the current datasets can have local ring, star, and chain sub-network structures; and (2) both city-to-city and firm-to-firm one-mode networks, which are obtained from the two-mode city-firm network, could provide insights about the geographies of contemporary globalization and its networked dimensions.

2. WCN researchers can reduce data collection subjectivity and structural determined features by removing the inclusion criteria on the number of cities a firm should have a presence in. Including small firms and thus having smaller possible clique size is not necessary, as the implicit idea is that major firms with sizable presence and power structure the WCN at large.

3. In line with Neal (2011), we suggest using actual SNA techniques, which are devised to examine two-mode networks directly. Despite the profound impact of Taylor’s (2001) paper on the WCN literature, it can be noted that few studies have realized the potential in that most quantitative analyses retreat into the use of standard data analysis techniques such as cluster analysis and factor analysis, which – although useful on their own terms - do not fully use the specification of the WCN as a fully-fledged network.

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NOTES

^* Xingjian Liu, University of Cambridge,Cambridge, UK, email: xl306@cam.ac.uk

^** Ben Derudder, Department of Geography, Ghent University, Belgium, email: ben.derudder@ugent.be

1. There has been an earlier critical appraisal of the IWCN model by Nordlund (2004), but in our reading his critique has been effectively tackled by Taylor (2004).

2. As of 14 July 2011, Taylor’s (2001) paper has been cited 77 times in papers listed in the ISI Web of Science, making it one of the most-cited papers both in this research domain and in Geographical Analysis.

3. Our assumption is that Taylor (2001) did not explicitly follow up on the relevance of his specification of the WCN as a two-mode network because at that time his overall purpose was to specify the WCN so that its geographical outline can be analysed as any other (social) network (see, for instance, Derudder and Taylor, 2005).

4. Neal (2011) himself concedes that these structures usually serve as local ‘simple structures’ and form a bigger WCN by ‘overlapping in various combinations’.