Measuring the dissimilarity of multiplex networks: An empirical study of international trade 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.