# Non-Euclidean Mixture Model for Social Network Embedding

arXiv: https://arxiv.org/abs/2411.04876 · HTML: https://mlsanity.com/paper/2411.04876/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Builds on (most cited first, 22 of 22)

- [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)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Homogeneous Network Embedding for Massive Graphs via Reweighted Personalized PageRank](https://mlsanity.com/paper/1906.06826/) (2019)
- [UUKG: Unified Urban Knowledge Graph Dataset for Urban Spatiotemporal Prediction](https://mlsanity.com/paper/2306.11443/) (2023)
- [Link Prediction with Attention Applied on Multiple Knowledge Graph Embedding Models](https://mlsanity.com/paper/2302.06229/) (2023)
- [CenGCN: Centralized Convolutional Networks with Vertex Imbalance for Scale-Free Graphs](https://mlsanity.com/paper/2202.07826/) (2022)
- [Dual-Geometric Space Embedding Model for Two-View Knowledge Graphs](https://mlsanity.com/paper/2209.08767/) (2022)
- [Challenging Low Homophily in Social Recommendation](https://mlsanity.com/paper/2401.14606/) (2024)
- [Collaborative Graph Neural Networks for Attributed Network Embedding](https://mlsanity.com/paper/2307.11981/) (2023)
- [Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of the Same Coin](https://mlsanity.com/paper/2309.10013/) (2023)
- [Hyperbolic Heterogeneous Graph Attention Networks](https://mlsanity.com/paper/2404.09456/) (2024)
- [RCoCo: Contrastive Collective Link Prediction across Multiplex Network in Riemannian Space](https://mlsanity.com/paper/2403.01864/) (2024)

## Built on by (most cited first, 4 of 4)

- [Hypergraph clustering using Ricci curvature: an edge transport perspective](https://mlsanity.com/paper/2412.15695/) (2024)
- [Transfer learning under latent space model](https://mlsanity.com/paper/2509.15797/) (2025)
- [Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification](https://mlsanity.com/paper/2603.29148/) (2026)
- [HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry](https://mlsanity.com/paper/2608.11768/) (2026)

## Abstract (arXiv)

It is largely agreed that social network links are formed due to either homophily or social influence. Inspired by this, we aim at understanding the generation of links via providing a novel embedding-based graph formation model. Different from existing graph representation learning, where link generation probabilities are defined as a simple function of the corresponding node embeddings, we model the link generation as a mixture model of the two factors. In addition, we model the homophily factor in spherical space and the influence factor in hyperbolic space to accommodate the fact that (1) homophily results in cycles and (2) influence results in hierarchies in networks. We also design a special projection to align these two spaces. We call this model Non-Euclidean Mixture Model, i.e., NMM. We further integrate NMM with our non-Euclidean graph variational autoencoder (VAE) framework, NMM-GNN. NMM-GNN learns embeddings through a unified framework which uses non-Euclidean GNN encoders, non-Euclidean Gaussian priors, a non-Euclidean decoder, and a novel space unification loss component to unify distinct non-Euclidean geometric spaces. Experiments on public datasets show NMM-GNN significantly outperforms state-of-the-art baselines on social network generation and classification tasks, demonstrating its ability to better explain how the social network is formed.