Structural Compactness as a Complementary Criterion for Explanation Quality

In the evaluation of attribution quality, the quantitative assessment of explanation legibility is particularly difficult, as it is influenced by varying shapes and internal organization of attributions not captured by simple statistics. To address this issue, we introduce Minimum Spanning Tree Compactness (MST-C), a graph-based structural metric that captures higher-order geometric properties of attributions, such as spread and cohesion. These components are combined into a single score that evaluates compactness, favoring attributions with salient points spread across a small area and spatially organized into few but cohesive clusters. We show that MST-C reliably distinguishes between explanation methods, exposes fundamental structural differences between models, and provides a robust, self-contained diagnostic for explanation compactness that complements existing notions of attribution complexity.