strength s$_{i}$ (Barrat et al. 2004). The strength distribution can also be approximated by a power law P ( s ) ∝ s − η with η = 1 . 02 ± 0 . 17, meaning that a small number of ports handle huge amounts of cargo (Fig. 2c). The determination of power law relationships by line fitting has been strongly criticised (e.g. Newman 2005, Clauset et al. 2009), therefore we analysed the distributions with model selection by Akaike weights (Burnham & Anderson 1998). Our results confirm that a power law is a better fit than an exponential or a log-normal distribution for P ( w ) and P ( s ), but not P ( k ) (see Electronic Supplementary Material). These findings agree well with the concept of hubs-spokes networks (Notteboom 2004) that were proposed for cargo traffic, for example in Asia (Robinson 1998). There are a few large, highly connected ports through which all smaller ports transact their trade. This scale-free property makes the ship trade network prone to the spreading and persistence of bioinvasive organisms (e.g. Pastor-Satorras & Vespignani 2001). The average nearest neighbors’s degrees, a measure of network assortativity, additionally underline the hubs- spokes property of cargo ship traffic (see Electronic Supplementary Material). 

Strengths and degrees of the ports are related according to the scaling relation 〈 s ( k ) 〉 ∝ k 1 . 46 ± 0 . 1 (95% CI for SMA regression, Warton et al. 2006). Hence, the strength of a port grows generally faster than its degree (Fig. 2d). In other words, highly connected ports not only have many links, but their links also have a higher than average weight. This observation agrees with the fact that busy ports are better equipped to handle large ships with large amounts of cargo. A similar result, 〈 s ( k ) 〉 ∝ k 1 . 5 ± 0 . $^{1}$, was found for airports (Barrat et al. 2004), which may hint at a general pattern in transportation networks. In the light of bioinvasion, these results underline empirical findings that big ports are more heavily invaded because of increased propagule pressure by ballast water of more and larger ships (Mack et al. 2000, Williamson 1996, see e.g. Cohen & Carlton 1998). 

A further indication of the importance of a node is its betweenness centrality (Freeman 1979, Newman 2004). The betweenness of a port is the number of topologically shortest directed paths in the network that pass through this port. In Fig. 1b we plot and list the most central ports. Generally speaking, centrality and degree are strongly correlated (Pearson’s correlation coefficient: 0 . 81), but in individual cases other factors can also play a role. The Panama and Suez Canal, for instance, are shortcuts to avoid long passages around South America and Africa. Other ports have a high centrality because they are visited by a large number of ships (e.g. Shanghai) whereas others gain their status primarily by being 

