Node2Vec

node2vec is a scalable feature learning framework for networks that generates continuous vector representations for nodes. It combines biased random walks with a skip-gram model to preserve network neighborhoods in a low-dimensional space, enabling various downstream tasks such as link prediction and node classification.

The core idea is to sample node sequences with biased random walks. node2vec uses a second-order random walk that is guided by two parameters, p and q, which control the likelihood of revisiting a node and exploring the neighborhood. This creates a spectrum between breadth-first search and depth-first search behaviors, allowing the method to capture both local clustering and broader structural roles within the graph.

Training is performed by applying the skip-gram objective to the sequences produced by the biased walks. The model learns vector representations by predicting nearby nodes within a window in the walk, typically using negative sampling or hierarchical softmax. The resulting node embeddings reflect both the network’s local structure and its more global topology, as dictated by the walk strategy and hyperparameters.

Node2vec embeddings are applicable to weighted and unweighted graphs and can be used for a range of tasks, including link prediction, node classification, clustering, and visualization. The method is often contrasted with DeepWalk, which uses uniform random walks; node2vec’s biased sampling provides greater flexibility to capture diverse network patterns.

Limitations include sensitivity to hyperparameters such as walk length, number of walks per node, embedding dimension, and the p and q settings. It is suitable for moderately large graphs and benefits from implementations that support efficient sampling and optimization.