Network community detection via neural embeddings

TL;DR

This paper demonstrates that node2vec, a neural graph embedding method, effectively encodes network communities into separable clusters, closely related to spectral embeddings, and performs well on various sparse graph models.

Contribution

It reveals the spectral nature of node2vec embeddings and explains how neural embeddings encode community structure, advancing understanding of neural graph embedding mechanisms.

Findings

Node2vec encodes communities into separable clusters.

Embedding aligns with spectral embedding via Laplacian eigenvectors.

Effective on sparse stochastic blockmodel and degree-heterogeneous networks.

Abstract

Recent advances in machine learning research have produced powerful neural graph embedding methods, which learn useful, low-dimensional vector representations of network data. These neural methods for graph embedding excel in graph machine learning tasks and are now widely adopted. However, how and why these methods work -- particularly how network structure gets encoded in the embedding -- remain largely unexplained. Here, we show that node2vec -- shallow, linear neural network -- encodes communities into separable clusters better than random partitioning down to the information-theoretic detectability limit for the stochastic block models. We show that this is due to the equivalence between the embedding learned by node2vec and the spectral embedding via the eigenvectors of the symmetric normalized Laplacian matrix. Numerical simulations demonstrate that node2vec is capable of learning communities on sparse graphs generated by the stochastic blockmodel, as well as on sparse degree-heterogeneous networks. Our results highlight the features of graph neural networks that enable them to separate communities in embedding space.