Multilayer-Dynamic Network Clustering with Application to World Trade Data

The rapid development of global economic integration has made international trade increasingly dynamic and interdependent.

The real-world trade data sets, such as the FAO dataset, can be naturally represented as a \emph{multilayer-dynamic network} where countries are treated as nodes, trade flows between countries are represented by edges, and different products correspond to different layers.

Therefore, an important problem is how to identify evolving community structures in the multilayer-dynamic trade network.

However, most existing methods are designed for static multilayer networks or single-layer dynamic networks, leaving the community detection in multilayer-dynamic networks largely unexplored.

Motivated by this problem, we study community detection in multilayer-dynamic networks, allowing the community structure to vary across both layers and time.

We propose a novel method, \emph{MuDySC} (Multilayer-Dynamic Spectral Clustering), which smooths the eigenspace projection matrices across adjacent time points and across layers at the same time point.

We develop an efficient alternating iterative algorithm for solving the resulting optimization problem and establish its convergence to the global optimum under mild conditions.

We further apply MuDySC to the FAO data.

The analysis reveals clear asymmetry between export and import community structures and highlights both persistent and shifting trade positions of major countries.