# PANE: scalable and effective attributed network embedding

arXiv: https://arxiv.org/abs/2009.00826 · HTML: https://mlsanity.com/paper/2009.00826/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2020.

## Built on by (most cited first, 23 of 23)

- [Fully-inductive Node Classification on Arbitrary Graphs](https://mlsanity.com/paper/2405.20445/) (2024)
- [Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models](https://mlsanity.com/paper/2506.14291/) (2025)
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- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [Effective Clustering on Large Attributed Bipartite Graphs](https://mlsanity.com/paper/2405.11922/) (2024)
- [Spectral Subspace Clustering for Attributed Graphs](https://mlsanity.com/paper/2411.11074/) (2024)
- [View Space: Learning Representation across Arbitrary Graphs](https://mlsanity.com/paper/2512.11561/) (2025)
- [Towards Efficient Training of Graph Neural Networks: A Multiscale Approach](https://mlsanity.com/paper/2503.19666/) (2025)
- [How Low Can You Go? Searching for the Intrinsic Dimensionality of Complex Networks using Metric Node Embeddings](https://mlsanity.com/paper/2503.01723/) (2025)
- [Modality-free Graph In-context Alignment](https://mlsanity.com/paper/2603.13434/) (2026)
- [DiGRAF: Diffeomorphic Graph-Adaptive Activation Function](https://mlsanity.com/paper/2407.02013/) (2024)
- [Adaptive Local Clustering over Attributed Graphs](https://mlsanity.com/paper/2503.20488/) (2025)
- [Effective Clustering for Large Multi-Relational Graphs](https://mlsanity.com/paper/2508.17388/) (2025)
- [GILT: An LLM-Free, Tuning-Free Graph Foundational Model for In-Context Learning](https://mlsanity.com/paper/2510.04567/) (2025)
- [PGB: A PubMed Graph Benchmark for Heterogeneous Network Representation Learning](https://mlsanity.com/paper/2305.02691/) (2023)
- [Robustness Verification of Graph Neural Networks Via Lightweight Satisfiability Testing](https://mlsanity.com/paper/2510.18591/) (2025)
- [SPGCL: Simple yet Powerful Graph Contrastive Learning via SVD-Guided Structural Perturbation](https://mlsanity.com/paper/2602.00064/) (2026)
- [Community Concealment from Graph Neural Networks](https://mlsanity.com/paper/2602.12250/) (2026)
- [Can Graph Foundation Models Generalize Over Architecture?](https://mlsanity.com/paper/2603.22984/) (2026)
- [The Impact of Dimensionality on the Stability of Node Embeddings](https://mlsanity.com/paper/2604.08492/) (2026)
- [Neural Message Passing on Structural Interaction Graphs for Fully-Inductive Graph Neural Networks](https://mlsanity.com/paper/2608.08567/) (2026)

## Abstract (arXiv)

Given a graph G where each node is associated with a set of attributes, attributed network embedding (ANE) maps each node v in G to a compact vector Xv, which can be used in downstream machine learning tasks. Ideally, Xv should capture node v's affinity to each attribute, which considers not only v's own attribute associations, but also those of its connected nodes along edges in G. It is challenging to obtain high-utility embeddings that enable accurate predictions; scaling effective ANE computation to massive graphs pushes the difficulty of the problem to a whole new level. Existing solutions largely fail on such graphs, leading to prohibitive costs, low-quality embeddings, or both. This paper proposes PANE, an effective and scalable approach to ANE computation for massive graphs that achieves state-of-the-art result quality on multiple benchmark datasets. PANE obtains high scalability and effectiveness through 3 main algorithmic designs. First, it formulates the learning objective based on a novel random walk model for attributed networks. Second, PANE includes a highly efficient solver for the above optimization problem, whose key module is a carefully designed initialization of the embeddings, which drastically reduces the number of iterations required to converge. Finally, PANE utilizes multi-core CPUs through non-trivial parallelization of the above solver, which achieves scalability while retaining the high quality of the resulting embeddings. The performance of PANE depends upon the number of attributes in the input network. To handle large networks with numerous attributes, we further extend PANE to PANE++. Extensive experiments, comparing 10 existing approaches on 8 real datasets, demonstrate that PANE and PANE++ consistently outperform all existing methods in terms of result quality, while being orders of magnitude faster.