node2vecs

Node2vec is a network representation learning method for producing continuous feature vectors for nodes in graphs. Introduced by Aditya Grover and Jure Leskovec in 2016, it generalizes earlier approaches by using biased random walks to capture diverse network neighborhoods and applying a skip-gram model to learn embeddings. The method is designed to balance structural equivalence and community similarity by adjusting how walks explore the graph.

A central idea of node2vec is to generate short random walks on the graph and treat the sequence of nodes as a sentence, then learn node embeddings that maximize the likelihood of preserving node neighborhoods within those walks. The walks are biased by two hyperparameters, p and q, which control the likelihood of revisiting a node (return) and exploring outward from the current region (inout). By tuning p and q, node2vec can interpolate between behavior similar to depth-first search (DFS) and breadth-first search (BFS), enabling the capture of different network properties.

Training typically uses a skip-gram objective, as in Word2Vec, with negative sampling or hierarchical softmax. The resulting vectors place nodes with similar network roles or community structures close in the embedding space, enabling downstream tasks such as link prediction, node classification, clustering, and visualization. Node2vec is designed to be scalable to large graphs and leverages stochastic optimization for efficiency.

In common usage, node2vec refers to the algorithm itself, while the plural form node2vecs may be used colloquially to denote multiple embeddings or runs. The method has inspired numerous extensions and alternatives in network representation learning, including adaptations for heterogeneous networks and higher-order relational patterns.