# WGCN: Graph Convolutional Networks with Weighted Structural Features

arXiv: https://arxiv.org/abs/2104.14060 · HTML: https://mlsanity.com/paper/2104.14060/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 55 references that are in the map.
- First posted on arXiv 29 Apr 2021.

## Builds on (most cited first, 30 of 35)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Streaming Graph Neural Networks](https://mlsanity.com/paper/1810.10627/) (2018)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Covariant Compositional Networks For Learning Graphs](https://mlsanity.com/paper/1801.02144/) (2018)
- [Attention Models in Graphs: A Survey](https://mlsanity.com/paper/1807.07984/) (2018)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [VGCN-BERT: Augmenting BERT with Graph Embedding for Text Classification](https://mlsanity.com/paper/2004.05707/) (2020)
- [Detecting Beneficial Feature Interactions for Recommender Systems](https://mlsanity.com/paper/2008.00404/) (2020)
- [Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space](https://mlsanity.com/paper/1602.06522/) (2016)

## Built on by (most cited first, 12 of 12)

- [GraFN: Semi-Supervised Node Classification on Graph with Few Labels via Non-Parametric Distribution Assignment](https://mlsanity.com/paper/2204.01303/) (2022)
- [Neural Graph Matching based Collaborative Filtering](https://mlsanity.com/paper/2105.04067/) (2021)
- [CSGCL: Community-Strength-Enhanced Graph Contrastive Learning](https://mlsanity.com/paper/2305.04658/) (2023)
- [Detecting Arbitrary Order Beneficial Feature Interactions for Recommender Systems](https://mlsanity.com/paper/2206.13764/) (2022)
- [Spectral Transform Forms Scalable Transformer](https://mlsanity.com/paper/2111.07602/) (2021)
- [AsyncET: Asynchronous Learning for Knowledge Graph Entity Typing with Auxiliary Relations](https://mlsanity.com/paper/2308.16055/) (2023)
- [Towards Bridging Review Sparsity in Recommendation with Textual Edge Graph Representation](https://mlsanity.com/paper/2508.01128/) (2025)
- [RRLFSOR: An Efficient Self-Supervised Learning Strategy of Graph Convolutional Networks](https://mlsanity.com/paper/2108.07481/) (2021)
- [Graph Decipher: A transparent dual-attention graph neural network to understand the message-passing mechanism for the node classification](https://mlsanity.com/paper/2201.01381/) (2022)
- [IB-Net: Initial Branch Network for Variable Decision in Boolean Satisfiability](https://mlsanity.com/paper/2403.03517/) (2024)
- [Knowledge Probing for Graph Representation Learning](https://mlsanity.com/paper/2408.03877/) (2024)
- [GS-Quant: Granular Semantic and Generative Structural Quantization for Knowledge Graph Completion](https://mlsanity.com/paper/2604.21649/) (2026)

## Abstract (arXiv)

Graph structural information such as topologies or connectivities provides valuable guidance for graph convolutional networks (GCNs) to learn nodes' representations. Existing GCN models that capture nodes' structural information weight in- and out-neighbors equally or differentiate in- and out-neighbors globally without considering nodes' local topologies. We observe that in- and out-neighbors contribute differently for nodes with different local topologies. To explore the directional structural information for different nodes, we propose a GCN model with weighted structural features, named WGCN. WGCN first captures nodes' structural fingerprints via a direction and degree aware Random Walk with Restart algorithm, where the walk is guided by both edge direction and nodes' in- and out-degrees. Then, the interactions between nodes' structural fingerprints are used as the weighted node structural features. To further capture nodes' high-order dependencies and graph geometry, WGCN embeds graphs into a latent space to obtain nodes' latent neighbors and geometrical relationships. Based on nodes' geometrical relationships in the latent space, WGCN differentiates latent, in-, and out-neighbors with an attention-based geometrical aggregation. Experiments on transductive node classification tasks show that WGCN outperforms the baseline models consistently by up to 17.07% in terms of accuracy on five benchmark datasets.