A Study On The Correlations Between Layers In Multiplex International Networks

In recent years, multiplex networks are becoming a research focus in the domain of complex networks. Discovering significant correlations between layers in multiplex networks can provide an insight to their structures. In this study, we propose some methods to measure the dissimilarities of different layers in directed and weighted multiplex networks. The dissimilarity is defined on two levels: node level and layer level. The node dissimilarity is computed based on the distance of the probability distribution of its link weights vectors in different layers; and the layer-level dissimilarity is the weighted sum of the nodes'dissimilarities. Furthermore, the dissimilarity is disintegrated into the connection-based dissimilarity and the weight-based dissimilarity, which represent the topological structure changes and the link weight changes,respectively. The proposed methods are applied to international trade networks.Through the experiment analysis, we get some findings:First, the shapes of nodes' Export-dissimilarity distributions of different pairs of commodities are different, and there are no significant changes for most Export-dissimilarity matrices in different years; second,the Import-dissimilarity matrices between commodity-pair layers in ITN have some similar properties as the Export-dissimilarity matrices; third,the dissimilarities between layers depend on the strength sequences greatly; Fourth, there is significantly linear relationship between structural dissimilarity and time difference for all of the commodities. These findings can help us better understand structures and changes of global economy.