# Optimization-Free Graph Embedding via Distributional Kernel for Community Detection

arXiv: https://arxiv.org/abs/2602.13634 · HTML: https://mlsanity.com/paper/2602.13634/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 52 references that are in the map.
- First posted on arXiv 14 Feb 2026.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [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)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Adaptive Graph Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2007.01594/) (2020)
- [Node Dependent Local Smoothing for Scalable Graph Learning](https://mlsanity.com/paper/2110.14377/) (2021)
- [Faster Kernels for Graphs with Continuous Attributes via Hashing](https://mlsanity.com/paper/1610.00064/) (2016)
- [Community detection in node-attributed social networks: a survey](https://mlsanity.com/paper/1912.09816/) (2019)
- [Revisiting Modularity Maximization for Graph Clustering: A Contrastive Learning Perspective](https://mlsanity.com/paper/2406.14288/) (2024)
- [Nearest-Neighbour-Induced Isolation Similarity and its Impact on Density-Based Clustering](https://mlsanity.com/paper/1907.00378/) (2019)
- [Siamese Attribute-missing Graph Auto-encoder](https://mlsanity.com/paper/2112.04842/) (2021)

## Abstract (arXiv)

Neighborhood Aggregation Strategy (NAS) is a widely used approach in graph embedding, underpinning both Graph Neural Networks (GNNs) and Weisfeiler-Lehman (WL) methods. However, NAS-based methods are identified to be prone to over-smoothing-the loss of node distinguishability with increased iterations-thereby limiting their effectiveness. This paper identifies two characteristics in a network, i.e., the distributions of nodes and node degrees that are critical for expressive representation but have been overlooked in existing methods. We show that these overlooked characteristics contribute significantly to over-smoothing of NAS-methods. To address this, we propose a novel weighted distribution-aware kernel that embeds nodes while taking their distributional characteristics into consideration. Our method has three distinguishing features: (1) it is the first method to explicitly incorporate both distributional characteristics; (2) it requires no optimization; and (3) it effectively mitigates the adverse effects of over-smoothing, allowing WL to preserve node distinguishability and expressiveness even after many iterations of embedding. Experiments demonstrate that our method achieves superior community detection performance via spectral clustering, outperforming existing graph embedding methods, including deep learning methods, on standard benchmarks.