The collective movement of stock prices harbors complex interdependencies that are conventionally simplified only through a linear lens. This paper explores computed structural network representations in the Indonesian capital market by testing the limits of Pearson correlation and Mutual Information (MI) in unveiling the spectral dynamics of the market. Across 2,328 rolling observation windows from 2015 to 2025, we examine 24 methodological configurations that combine three dependency estimators (Pearson, MI adaptive binning, and MI-kNN), two graph filtering schemes (Minimum Spanning Tree/MST and Planar Maximally Filtered Graph/PMFG), and four community decoders. The empirical results unveil a fundamental reality: topological richness does not always resonate with sectoral classification precision. The Pearson, MST, and Infomap configuration is shown to remain the most robust foundation for recovering conventional sectoral taxonomy. Nevertheless, when deeper observation demands the exposition of local structures and the weave of heterogeneous communities, the architectural relaxation through PMFG demonstrates its superiority. In the realm of residual information detection, MI adaptive binning appears far more proportional than kNN; histogram-based regularization successfully tames empirical noise without sweeping away traces of non-linear dependency. Ultimately, the synergy of MI and PMFG is not positioned to dethrone the dominance of linear correlation, but rather to provide an essential analytical lens for excavating hidden economic sub-structures -- such as the cohesion of commodity regimes -- that have long transcended the rigid boundaries of the market's formal sectors.