Hidden community interlayer spillover detection in financial multilayer networks: Generalization of hierarchical clustering to multilayer networks

Interdependent networks structurally influence each other so that the source network imposes hidden community structures into the target network. We propose a mathematical model so that when introducing an interlayer similarity function we generalize hierarchical clustering approaches for multilayer networks. The proposed methodology shows how a "source" network influences the "target" network via structural spillovers that are hidden and are not detectable by conventional community detection methods. The methodology reveals evidence that hidden interlayer interactions consequently generate hidden links on the target network. These hidden links construct hidden community structures on the target network (imposed from the source network) that are distinct from the community structures of the solo target network (without the presence of the source network). This model applies to systems with hidden interlayer interactions, such as, e.g., covert criminal groups, inter-platform social network interactions, scientific research groups, and financial markets. Financial markets are well known for complicated endogenous and exogenous, but often hidden, not to say the least, asymmetric layer interactions. We implement our model on multilayer financial networks: in particular, we find that trading value logarithmic changes (source) impose hidden community structures on the price return network (target). The main finding is that adding another relevant layer, such as the trading value layer, adds more information to systemic behaviors throughout the price return network. Dismissing it may yield less systemic information and underestimation of systemic risk because the footprint of some structures on the target network originated from another layer and is not detectable by singling out the target layer. As an empirical application, we exploit the methodology to define another perspective on portfolio diversification.