Statistical properties of links of network: A survey on the shipping lines of Worldwide Marine Transport Network

Node properties and node importance identification of networks have been vastly studied in the last decades. While in this work, we analyze the links' properties of networks by taking the Worldwide Marine Transport Network (WMTN) as an example, i.e., statistical properties of the shipping lines of WMTN have been investigated in various aspects: Firstly, we study the feature of loops in the shipping lines by defining the line saturability. It is found that the line saturability decays exponentially with the increase of line length. Secondly, to detect the geographical community structure of shipping lines, the Label Propagation Algorithm with compression of Flow (LPAF) and Multi-Dimensional Scaling (MDS) method are employed, which show rather consistent communities. Lastly, to analyze the redundancy property of shipping lines of different marine companies, the multilayer networks are constructed by aggregating the shipping lines of different marine companies. It is observed that the topological quantities, such as average degree, average clustering coefficient, etc., increase smoothly when marine companies are randomly merged (randomly choose two marine companies, then merge the shipping lines of them together), while the relative entropy decreases when the merging sequence is determined by the Jensen-Shannon distance (choose two marine companies when the Jensen-Shannon distance between them is the lowest). This indicates the low redundancy of shipping lines among different marine companies.