The proposed framework integrates Manifold Learning strategies with Rank-based Interpretable Graph Embeddings to provide interpretability while maintaining low dimensionality. ^[1] Graph Neural Networks (GNNs) are designed to apply neural networks to graph structures, which represent a set of objects along with the relationships between them. ^[2] The approach characterizes contextual information of the dataset through manifold analysis and subsequently generates sparse, self-explainable embeddings. ^[3] The authors note an 'Interpretability Gap' where existing representations often lack alignment with human cognition. ^[4] The paper identifies a 'Geometric Gap' where traditional pairwise measures fail to capture the intrinsic geometry of the dataset manifold in visual information modeling. ^[5] GNNs can be used to classify individual nodes or edges, as well as classify a graph as a whole. ^[6] Graph Convolutional Networks (GCN) apply the concept of convolutions from images to graphs by combining a node with its adjacent nodes to produce new features. ^[7] The update rule for GCNs involves an adjacency matrix A, a feature matrix H, and a learnable linear transformation matrix W, followed by a non-linear transformation σ. ^[8]