Empirical research on world cities often draws on Taylor's (2001) notion of an 'interlocking network model', in which office networks of globalized service firms are assumed to shape the spatialities of urban networks. In spite of its many merits, this approach is limited because the resultant adjacency matrices are not really fit for network-analytic calculations. We therefore propose a fresh analytical approach using a primary linkage algorithm that produces a one-mode directed graph based on Taylor's two-mode city/firm network data. The procedure has the advantage of creating less dense networks when compared to the interlocking network model, while nonetheless retaining the network structure apparent in the initial dataset. We randomize the empirical network with a bootstrapping simulation approach, and compare the simulated parameters of this null-model with our empirical network parameter (i.e. betweenness centrality). We find that our approach produces results that are comparable to those of the standard interlocking network model. However, because our approach is based on an actual graph representation and network analysis, we are able to assess cities' position in the network at large. For instance, we find that cities such as Tokyo, Sydney, Melbourne, Almaty and Karachi hold more strategic and valuable positions than suggested in the interlocking networks as they play a bridging role in connecting cities across regions. In general, we argue that our graph representation allows for further and deeper analysis of the original data, further extending world city network research into a theory-based empirical research approach.