The distribution functions of vessel calls and port connectivity in the global cargo ship network

Abstract

Characterizing the connectivity of nodes in economic and technological networks is of key interest to assess their role and function. Here we study the distributions of vessel calls and the ports’ degrees (i.e. the number of other ports that a port is directly linked with) in the network of worldwide cargo ship movements – the main transport network for world trade – for twenty different years between 1890 and 2008. We compare the Akaike information criterion and goodness- of-fit statistics of various common probabilistic models. Simple power laws, once believed to be a universal feature of degree distributions in complex networks, are inadequate to fit the data. Other subexponential distributions, such as lognormal or Weibull distributions, perform consistently better. Cargo ship traffic has thus for the entire study period been heavy-tailed with some ports being significantly busier than the average, but the distribution is not scale-free. Vuong’s likelihood ratio test confirms that since 1975 a Weibull distribution can be regarded as a plausible null hypothesis. Lognormal distributions perform well for most years in Kolmogorov-Smirnov and Anderson-Darling tests for the call distribution. The Gini coefficient of the distribution has slightly, but statistically significantly, decreased over the study period, highlighting a tendency towards a more polycentric distribution in port traffic.