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SIMPLE SPECTRAL GRAPH CONVOLUTION

Hao Zhu, Piotr Koniusz · 2026 · 69 citationsRead the paper

Graph Convolutional Networks (GCNs) are leading methods for learning graph representations. However, without specially designed architectures, the performance of GCNs degrades quickly with increased depth. As the aggregated neighborhood size and neural network depth are two completely orthogonal aspects of graph representation, several methods focus on summarizing the neighborhood by aggregating K-hop neighborhoods of nodes while using shallow neural networks. However, these methods still encounter oversmoothing, and suffer from high computation and storage costs. In this paper, we use a modified Markov Diffusion Kernel to derive a variant of GCN called Simple Spectral Graph Convolution (S2GC). Our spectral analysis shows that our simple spectral graph convolution used in S2GC is a trade-off of low- and high-pass filter bands which capture the global and local contexts of each node. We provide two theoretical claims which demonstrate that we can aggregate over a sequence of increasingly larger neighborhoods compared to competitors while limiting severe oversmoothing. Our experimental evaluations show that S2GC with a linear learner is competitive in text and node classification tasks. Moreover, S2GC is comparable to other state-of-the-art methods for node clustering and community prediction tasks.

What the full text shows

Working prototype
  • S2GC achieves higher node classification accuracy than GCN, GAT, and SGC on Cora, Citeseer, and Pubmed. — 83.5% (Cora), 73.6% (Citeseer), 80.2% (Pubmed) accuracy (Semi-supervised node classification with K=16, alpha=0.05)
  • S2GC outperforms other attributed graph clustering methods (GAE, VGAE, ARGE, ARVGE, AGC) across four datasets. — 69.6% (Cora), 69.11% (Citeseer), 70.98% (Pubmed), 70.28% (Wiki) accuracy (Node clustering task using both node features and graph structures)
  • S2GC maintains higher accuracy at greater depths (K) compared to GCN and SGC, mitigating oversmoothing. — 83.5% accuracy at K=16 vs SGC's 79.0% and GCN's 64.9% on Cora (Linear model on Cora dataset)
  • S2GC+MLP (S2GC with a Multi-Layer Perceptron classifier) is the top performer on specific large-scale benchmarks. — Outperforms SGC on Mag, Arxiv, and Products (OGB node property prediction benchmark)
  • S2GC is competitive in text classification across five benchmark corpora. — 88.6% (20NG), 97.4% (R8), 94.5% (R52), 68.5% (Ohsumed), 76.7% (MR) accuracy (Document classification task)
Setup
Evaluated on Cora, Citeseer, Pubmed, Wiki, Reddit, Arxiv, Mag, Products, and five text corpora (MR, 20NG, Ohsumed, R52, R8).
How
The authors derive Simple Spectral Graph Convolution (S2GC) using a modified Markov Diffusion Kernel, which aggregates a sequence of increasingly larger neighborhoods (k=0 to K). This approach uses a linear projection as a filter to balance low- and high-pass spectral bands to capture both global and local contexts.
Limitations
S2GC alone cannot outperform GCN or GraphSage on Arxiv and Products datasets without an MLP classifier. · Theoretical proofs for receptive field growth are based on Euclidean lattice graphs and approximations for non-Euclidean graphs.

Summarized by Gemma 4 from the open-access full text · 14 Oct 2026. Read it