How Heavy-Tailed is the Distribution of Global Cargo Ship Traffic?

Power laws, once believed to be a universal feature of degree distributions in complex networks, have come under attack in recent years. More sophisticated statistical analysis has often revealed other heavy-tailed distributions as more adequate descriptions of real-world data. Here we study degree and strength distributions of the network of worldwide cargo ship movements -- the main transport network for world trade -- from 14 different years between 1890 and 2008. We compare the Akaike information criterion of various common probabilistic models. In almost all cases, the Akaike weights identify a stretched exponential distribution as the most likely among the investigated models. Simple or truncated power laws, by contrast, do not capture the observations equally well. Cargo ship traffic is thus heavy-tailed with some ports being significantly busier than the average, but the distribution is not scale-free. The maximum-likelihood estimators indicate that the normalized distribution became increasingly shorter-tailed for one century. However, since the start of this millennium this trend appears to be reversing.