Many systems can be studied by representing them as multilayer networks. Multilayer networks are mathematical structures consisting of a set of objects with multiple kinds of possible relations...Show moreMany systems can be studied by representing them as multilayer networks. Multilayer networks are mathematical structures consisting of a set of objects with multiple kinds of possible relations between the objects. The study of various multilayer networks such as the network of international trade using statistical models with the assumption that the layers are independent leads to the observed overlap in the network being significantly different from the overlap predicted by the model. In an attempt to solve this issue we introduced interdependencies between the layers of a multilayer network in the model by explicitly including the overlap in our model. We then analytically derived the maximum likelihood equations for this model. Using numerical methods, we tested the validity of these obtained equations which proved to be highly accurate when compared to the numerical simulation data. Additionally, we have shown that the overlap of a network for a given number of links can be increased by either increasing the heterogeneity of the network or the value of the coupling parameter that we have introduced into the model. This allows us to create multiplexes with a specific amount of overlap for a given of number of links, given that it is within the theoretical limits. Finally, we conclude that the empirical overlap in the network of international trade is not merely a result of the correlation between the degrees of the different layers but requires a nonzero coupling between the layers in its modeling.Show less
