Maximum Edge Weight Click Problem: Application in Time Series Functional Networks

This study investigates the behavior of the Maximum Weight Edge Clique Problem as a tool for extracting dense subgraphs in functional networks constructed from multivariate time series. Adopting an Integer Linear Programming formulation, we characterize how the choice of association metrics (Pearson, Spearman, and Mutual Information) and the threshold θ affect the optimal clique under three synthetic regimes: high-frequency seasonality, low-frequency cycles with trend, and random walks. We further investigate the effect of restricting clique cardinality through different size constraints, analyzing how the imposition of an upper bound on the number of vertices affects the stability of the selected components. The results expose regimes where linear and non-linear metrics qualitatively diverge and reveal limitations of the approach in scenarios involving autocorrelated series.