Graph embedding is a family of representation-learning techniques that map the nodes, edges, or whole subgraphs of a graph into a continuous low-dimensional vector space while preserving structural and relational properties. The learned vectors place topologically or semantically similar elements close together, enabling machine-learning models to operate on graph-structured data. Methods range from random-walk approaches to neural graph encoders.
Overview
- Early graph-embedding methods adapted ideas from word embeddings: by sampling random walks over a graph and treating node sequences as sentences, models such as skip-gram learn vectors that capture neighbourhood structure. Later approaches use graph neural networks to aggregate information from a node’s neighbourhood through message passing, producing embeddings conditioned on both topology and node features. The resulting vectors serve as input to downstream classifiers, recommenders, and link predictors.
Mechanisms
- Random-walk sampling converts graph structure into sequences for skip-gram training.
- Matrix-factorisation methods decompose adjacency or proximity matrices.
- Graph neural networks aggregate neighbourhood features via message passing.
- Embeddings can target nodes, edges, or entire subgraphs.
- Objective functions preserve first-order and higher-order proximity.
Applications
- Node classification and community detection.
- Link prediction and recommendation systems.
- Knowledge-graph completion and reasoning.
- Anomaly and fraud detection in transaction graphs.
- Molecular and biological network analysis.