Graph Embedding

Graph embeddings are dense vector representations of graph nodes (and sometimes edges) that encode structural information from the graph. The goal is to map nodes to vectors such that nodes that are structurally similar in the graph are close together in vector space, bridging the gap between graph-structured and vector-based representations.

Key graph embedding methods include Node2Vec (generates random walks from each node and applies Word2Vec), DeepWalk (similar approach using uniform random walks), and Graph Convolutional Networks (GCN) which use neural message passing to aggregate information from node neighborhoods. The GCN update rule aggregates neighbor embeddings: h_v^(k+1) = activation(W * sum(h_u / |N(v)|)) for u in neighbors of v.

Graph embeddings are particularly valuable in hybrid RAG+KG systems because they enable similarity search over graph entities even without direct text matches. You can find entities similar to a query entity based on their structural role in the graph (e.g., finding similar companies based on their position in a supply chain graph), complementing text-based similarity search with structural similarity.