# Block Modeling-Guided Graph Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2112.13507 · HTML: https://mlsanity.com/paper/2112.13507/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 27 Dec 2021.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs](https://mlsanity.com/paper/2006.11468/) (2020)

## Built on by (most cited first, 30 of 32)

- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [RAW-GNN: RAndom Walk Aggregation based Graph Neural Network](https://mlsanity.com/paper/2206.13953/) (2022)
- [Node-oriented Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2212.03654/) (2022)
- [Understanding Heterophily for Graph Neural Networks](https://mlsanity.com/paper/2401.09125/) (2024)
- [HP-GMN: Graph Memory Networks for Heterophilous Graphs](https://mlsanity.com/paper/2210.08195/) (2022)
- [GraphRARE: Reinforcement Learning Enhanced Graph Neural Network with Relative Entropy](https://mlsanity.com/paper/2312.09708/) (2023)
- [Heterophily-Aware Graph Attention Network](https://mlsanity.com/paper/2302.03228/) (2023)
- [Spatial Heterophily Aware Graph Neural Networks](https://mlsanity.com/paper/2306.12139/) (2023)
- [Counterfactual Data Augmentation with Denoising Diffusion for Graph Anomaly Detection](https://mlsanity.com/paper/2407.02143/) (2024)
- [Shape-aware Graph Spectral Learning](https://mlsanity.com/paper/2310.10064/) (2023)
- [Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shifts](https://mlsanity.com/paper/2408.09490/) (2024)
- [SignGT: Signed Attention-based Graph Transformer for Graph Representation Learning](https://mlsanity.com/paper/2310.11025/) (2023)
- [NTFormer: A Composite Node Tokenized Graph Transformer for Node Classification](https://mlsanity.com/paper/2406.19249/) (2024)
- [Rethinking Tokenized Graph Transformers for Node Classification](https://mlsanity.com/paper/2502.08101/) (2025)
- [GCNH: A Simple Method For Representation Learning On Heterophilous Graphs](https://mlsanity.com/paper/2304.10896/) (2023)
- [GPatcher: A Simple and Adaptive MLP Model for Alleviating Graph Heterophily](https://mlsanity.com/paper/2306.14340/) (2023)
- [HeroFilter: Adaptive Spectral Graph Filter for Varying Heterophilic Relations](https://mlsanity.com/paper/2510.10864/) (2025)
- [HC-GST: Heterophily-aware Distribution Consistency based Graph Self-training](https://mlsanity.com/paper/2407.17787/) (2024)
- [Self-attention Dual Embedding for Graphs with Heterophily](https://mlsanity.com/paper/2305.18385/) (2023)
- [Propagation with Adaptive Mask then Training for Node Classification on Attributed Networks](https://mlsanity.com/paper/2206.10142/) (2022)
- [Neighborhood Convolutional Network: A New Paradigm of Graph Neural Networks for Node Classification](https://mlsanity.com/paper/2211.07845/) (2022)
- [Evolving Computation Graphs](https://mlsanity.com/paper/2306.12943/) (2023)
- [Boosting Graph Foundation Model from Structural Perspective](https://mlsanity.com/paper/2407.19941/) (2024)
- [Dual-Frequency Filtering Self-aware Graph Neural Networks for Homophilic and Heterophilic Graphs](https://mlsanity.com/paper/2411.11284/) (2024)
- [Directed Homophily-Aware Graph Neural Network](https://mlsanity.com/paper/2505.22362/) (2025)
- [Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing](https://mlsanity.com/paper/2507.20127/) (2025)
- [Gumbel-MPNN: Graph Rewiring with Gumbel-Softmax](https://mlsanity.com/paper/2508.17531/) (2025)
- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)
- [Bridging Computational Social Science and Deep Learning: Cultural Dissemination-Inspired Graph Neural Networks](https://mlsanity.com/paper/2509.19084/) (2025)

## Abstract (arXiv)

Graph Convolutional Network (GCN) has shown remarkable potential of exploring graph representation. However, the GCN aggregating mechanism fails to generalize to networks with heterophily where most nodes have neighbors from different classes, which commonly exists in real-world networks. In order to make the propagation and aggregation mechanism of GCN suitable for both homophily and heterophily (or even their mixture), we introduce block modeling into the framework of GCN so that it can realize "block-guided classified aggregation", and automatically learn the corresponding aggregation rules for neighbors of different classes. By incorporating block modeling into the aggregation process, GCN is able to aggregate information from homophilic and heterophilic neighbors discriminately according to their homophily degree. We compared our algorithm with state-of-art methods which deal with the heterophily problem. Empirical results demonstrate the superiority of our new approach over existing methods in heterophilic datasets while maintaining a competitive performance in homophilic datasets.