Link Prediction

Classical methods that compute a similarity metric between node pairs based on graph topology, serving as a fast, interpretable baseline for link likelihood.

• Common Neighbors: Counts shared neighbors; high overlap suggests a future link.
• Jaccard Coefficient: Normalizes common neighbors by total unique neighbors to penalize high-degree nodes.
• Adamic-Adar Index: Weighs common neighbors inversely by their degree, prioritizing rare, specific connections.
• Preferential Attachment: Scores node pairs by the product of their degrees, capturing the rich-get-richer effect in network growth.

Learns a low-dimensional vector representation for each node such that structural proximity is preserved in the embedding space. Link probability is computed as a similarity operation on the learned vectors.

• Node2Vec: Uses biased random walks to balance homophily and structural equivalence before training a Skip-gram model.
• DeepWalk: Performs uniform random walks to generate node sequences, treating them as sentences for word2vec-style training.
• Scoring Functions: Apply cosine similarity or a learned binary classifier to the Hadamard product of the two node embeddings to produce a link probability.

An unsupervised deep learning architecture where a GNN encoder compresses nodes into latent vectors, and a decoder reconstructs the adjacency matrix. Links with high reconstruction probability are predicted.

• Encoder: Typically a 2-layer GCN that generates node embeddings from features and topology.
• Decoder: Computes the inner product of two node embeddings followed by a sigmoid activation to output a link probability.
• Training Objective: Minimizes binary cross-entropy between the reconstructed and original adjacency matrices, treating observed edges as positive samples and randomly sampled non-edges as negatives.

A framework that frames link prediction as a binary subgraph classification problem, learning heuristics directly from the local enclosing graph around a target node pair.

• Enclosing Subgraph Extraction: Extracts the k-hop neighborhood surrounding the two target nodes.
• Node Labeling: Applies a Double-Radius Node Labeling (DRNL) function to tag nodes by their distance to the source and target, providing structural roles.
• GNN Classifier: Feeds the labeled subgraph into a GNN that outputs a probability score, enabling the model to learn complex structural heuristics beyond fixed similarity metrics.

Extends link prediction to dynamic graphs where edges are timestamped, forecasting future interactions based on historical temporal patterns.

• Temporal Graph Networks (TGN): Maintains a compressed memory state for each node that updates continuously as new events occur, enabling the model to predict the next interaction partner.
• Time-Encoding Functions: Uses sinusoidal or learnable Fourier features to encode continuous timestamps, allowing the model to reason about periodicity and recency.
• Application: Predicts which merchant an account will transact with next, flagging deviations from predicted behavior as anomalous.

Link prediction applied to heterogeneous knowledge graphs with typed edges, predicting missing relationship triples (head, relation, tail).

• TransE: Models relationships as translations in the embedding space: h + r ≈ t.
• RotatE: Models relations as rotations in complex vector space, capturing symmetry, inversion, and composition patterns.
• Financial KG Application: Predicts hidden beneficial ownership links or undisclosed relationships between shell companies and sanctioned entities by completing the graph of corporate registries and transaction flows.

The process of mapping discrete nodes to a low-dimensional, continuous vector space. The geometric proximity of these vectors preserves the structural and feature-based similarities of the original network. Link prediction is a primary downstream task used to evaluate the quality of these embeddings, as effective vectors should place nodes likely to form a connection near each other. Foundational algorithms include DeepWalk, Node2Vec, and GraphSAGE.

An unsupervised learning architecture that uses a Graph Neural Network encoder to produce latent node embeddings and a decoder to reconstruct the original graph adjacency matrix. For link prediction, the decoder scores the likelihood of an edge existing between two nodes based on their latent representations. A high reconstruction error for an existing edge, or a high predicted probability for a non-existent edge, can signal an anomaly or a future connection.

The fundamental computational paradigm in Graph Neural Networks where nodes iteratively exchange vectorized information with their neighbors to update their own hidden states. This mechanism captures relational dependencies crucial for link prediction. A model predicts a link between two nodes if their final, context-aware representations are highly similar, indicating they share significant topological and feature-based information.

A stochastic process that generates node sequences by randomly traversing graph edges. It serves as a foundational sampling strategy for learning structural node representations. In link prediction, the core heuristic is that nodes appearing in similar contexts within these short random walks should have similar embeddings, making them strong candidates for a predicted connection. Algorithms like Node2Vec use biased walks to balance local and global graph exploration.

A neural architecture designed for dynamic graphs where interactions occur chronologically. For link prediction, a TGN maintains a compressed memory state for each node that is updated after every new transaction. This allows the model to predict future links based on the evolving history of interactions, making it highly effective for forecasting the next transaction in a financial stream, rather than just analyzing a static snapshot.

The unsupervised partitioning of a graph into clusters of densely connected nodes. In the context of link prediction, the principle of homophily—that similar nodes connect—is key. If two nodes belong to the same detected community, the probability of a future or missing link between them is significantly higher. This is critical for identifying fraud rings where collusive links are intentionally hidden.