# CenGCN: Centralized Convolutional Networks with Vertex Imbalance for Scale-Free Graphs

arXiv: https://arxiv.org/abs/2202.07826 · HTML: https://mlsanity.com/paper/2202.07826/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 61 references that are in the map.
- First posted on arXiv 16 Feb 2022.

## Builds on (most cited first, 26 of 26)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [Random Walks: A Review of Algorithms and Applications](https://mlsanity.com/paper/2008.03639/) (2020)
- [Shifu2: A Network Representation Learning Based Model for Advisor-advisee Relationship Mining](https://mlsanity.com/paper/2008.07097/) (2020)
- [Multi-Component Graph Convolutional Collaborative Filtering](https://mlsanity.com/paper/1911.10699/) (2019)
- [MODEL: Motif-based Deep Feature Learning for Link Prediction](https://mlsanity.com/paper/2008.03637/) (2020)
- [Matching Algorithms: Fundamentals, Applications and Challenges](https://mlsanity.com/paper/2103.03770/) (2021)
- [Representation Learning for Scale-free Networks](https://mlsanity.com/paper/1711.10755/) (2017)
- [Spectral Clustering with Epidemic Diffusion](https://mlsanity.com/paper/1303.2663/) (2013)
- [The Interplay Between Dynamics and Networks: Centrality, Communities, and Cheeger Inequality](https://mlsanity.com/paper/1406.3387/) (2014)
- [Graph Filters and the Z-Laplacian](https://mlsanity.com/paper/1707.05851/) (2017)

## Built on by (most cited first, 14 of 14)

- [Graph Transformers: A Survey](https://mlsanity.com/paper/2407.09777/) (2024)
- [A Survey of Imbalanced Learning on Graphs: Problems, Techniques, and Future Directions](https://mlsanity.com/paper/2308.13821/) (2023)
- [Graph2text or Graph2token: A Perspective of Large Language Models for Graph Learning](https://mlsanity.com/paper/2501.01124/) (2025)
- [A Survey of Few-Shot Learning on Graphs: from Meta-Learning to Pre-Training and Prompt Learning](https://mlsanity.com/paper/2402.01440/) (2024)
- [Deep Outdated Fact Detection in Knowledge Graphs](https://mlsanity.com/paper/2402.03732/) (2024)
- [Non-Euclidean Mixture Model for Social Network Embedding](https://mlsanity.com/paper/2411.04876/) (2024)
- [Coupled Attention Networks for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2306.07114/) (2023)
- [Physics-Informed Graph Learning](https://mlsanity.com/paper/2202.10679/) (2022)
- [Fairness in Augmented Graph Learning: A Survey](https://mlsanity.com/paper/2504.21296/) (2025)
- [Balanced Graph Structure Information for Brain Disease Detection](https://mlsanity.com/paper/2401.00876/) (2023)
- [Graph Size-imbalanced Learning with Energy-guided Structural Smoothing](https://mlsanity.com/paper/2412.17591/) (2024)
- [Structural Imbalance Aware Graph Augmentation Learning](https://mlsanity.com/paper/2303.13757/) (2023)
- [Adversarial Curriculum Graph-Free Knowledge Distillation for Graph Neural Networks](https://mlsanity.com/paper/2504.00540/) (2025)
- [Data-Efficient Psychiatric Disorder Detection via Self-supervised Learning on Frequency-enhanced Brain Networks](https://mlsanity.com/paper/2509.10524/) (2025)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have achieved impressive performance in a wide variety of areas, attracting considerable attention. The core step of GCNs is the information-passing framework that considers all information from neighbors to the central vertex to be equally important. Such equal importance, however, is inadequate for scale-free networks, where hub vertices propagate more dominant information due to vertex imbalance. In this paper, we propose a novel centrality-based framework named CenGCN to address the inequality of information. This framework first quantifies the similarity between hub vertices and their neighbors by label propagation with hub vertices. Based on this similarity and centrality indices, the framework transforms the graph by increasing or decreasing the weights of edges connecting hub vertices and adding self-connections to vertices. In each non-output layer of the GCN, this framework uses a hub attention mechanism to assign new weights to connected non-hub vertices based on their common information with hub vertices. We present two variants CenGCND and CenGCNE, based on degree centrality and eigenvector centrality, respectively. We also conduct comprehensive experiments, including vertex classification, link prediction, vertex clustering, and network visualization. The results demonstrate that the two variants significantly outperform state-of-the-art baselines.