Preserving the Motif-Relevant Structure in Graph Neural Networks: An Entropy-Aware Study of Aggregation and Depth

Graph neural networks have shown strong potential for learning structural representations of biological networks. However, repeated message passing may blur local structural signals that are relevant for motif- and graphlet-based analysis. This paper investigates multilabel graphlet classification in protein-protein interaction networks to test whether GNNs can serve as reliable structural indicators for motif mining. We focus on two central design choices of message-passing neural networks: network depth, which determines the range of propagated neighborhood information, and neighborhood aggregation, which determines how this information is combined. We compare mean, max, and sum aggregation across increasing message-passing depths and across input feature sets with different levels of structural informativeness. Dropout and batch normalization are considered additional architectural factors. The resulting models are evaluated using multilabel classification metrics alongside homophily measures and Jensen-Shannon divergence to analyze how label distribution patterns impact prediction performance. Our approach acknowledges the structural limitations of GNNs but seeks to determine whether they can serve as reliable "hints" for the presence or absence of graphlets. To connect graphlet prediction with motif discovery, we further include a post hoc probability-guided motif search in which predicted graphlet probabilities are used to prioritize candidate regions for deterministic motif detection. This study provides an empirical analysis of how depth, aggregation, and feature informativeness interact in motif-oriented graph representation learning.