Introduction Accurate prediction of protein-protein interactions (PPIs) is crucial for understanding cellular functions and advancing drug development. Existing in-silico methods use direct sequence embeddings from Protein Language Models (PLMs). Others use Graph Neural Networks (GNNs) for 3D protein structures. This study explores less computationally intensive alternatives. We introduce a novel framework for downstream PPI prediction through link prediction. Methods We introduce a two-stage graph representation learning framework, ProtGram-DirectGCN. First, we developed ProtGram. This approach models a protein's primary structure as a hierarchy of globally inferred n-gram graphs. In these graphs, residue transition probabilities define edge weights. Each edge connects a pair of residues in a directed graph. The probabilities are aggregated from a large corpus of sequences. Second, we propose DirectGCN, a custom directed graph convolutional neural network. This model features a unique convolutional layer. It processes information through separate path-specific transformations: incoming, outgoing, and undirected. A shared transformation is also applied. These paths are combined via a learnable gating mechanism. We apply DirectGCN to ProtGram graphs to learn residue-level embeddings. These embeddings are pooled via attention to generate protein-level embeddings for prediction. Results We first established the efficacy of DirectGCN on standard node classification benchmarks. Its performance matches established methods on general datasets. The model excels at complex, directed graphs with dense, heterophilic structures. When applied to PPI prediction, the full ProtGram-DirectGCN framework delivers robust predictive power. This strong performance holds even with limited training data.