# Synergistic Graph Fusion via Encoder Embedding

arXiv: https://arxiv.org/abs/2303.18051 · HTML: https://mlsanity.com/paper/2303.18051/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 31 Mar 2023.

## Builds on (most cited first, 18 of 18)

- [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)
- [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)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Seeded graph matching for correlated ErdHos-R'enyi graphs](https://mlsanity.com/paper/1304.7844/) (2013)
- [One-Hot Graph Encoder Embedding](https://mlsanity.com/paper/2109.13098/) (2021)
- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [The Chi-Square Test of Distance Correlation](https://mlsanity.com/paper/1912.12150/) (2019)
- [Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detection](https://mlsanity.com/paper/2301.11290/) (2023)
- [Generalized Canonical Correlation Analysis for Classification](https://mlsanity.com/paper/1304.7981/) (2013)
- [The Exact Equivalence of Distance and Kernel Methods for Hypothesis Testing](https://mlsanity.com/paper/1806.05514/) (2018)
- [Manifold Matching using Shortest-Path Distance and Joint Neighborhood Selection](https://mlsanity.com/paper/1412.4098/) (2014)
- [Fast Embedding for JOFC Using the Raw Stress Criterion](https://mlsanity.com/paper/1502.03391/) (2015)
- [A Joint Graph Inference Case Study: the C.elegans Chemical and Electrical Connectomes](https://mlsanity.com/paper/1507.08376/) (2015)

## Built on by (most cited first, 6 of 6)

- [Refined Graph Encoder Embedding via Self-Training and Latent Community Recovery](https://mlsanity.com/paper/2405.12797/) (2024)
- [Encoder Embedding for General Graph and Node Classification](https://mlsanity.com/paper/2405.15473/) (2024)
- [Principal Graph Encoder Embedding and Principal Community Detection](https://mlsanity.com/paper/2501.14939/) (2025)
- [Efficient Graph Encoder Embedding for Large Sparse Graphs in Python](https://mlsanity.com/paper/2406.03726/) (2024)
- [Fast and Scalable Multi-Kernel Encoder Classifier](https://mlsanity.com/paper/2406.02189/) (2024)
- [Graph Neural Networks Powered by Encoder Embedding for Improved Node Learning](https://mlsanity.com/paper/2507.11732/) (2025)

## Abstract (arXiv)

In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic effect: for sufficiently large vertex size, the accuracy of vertex classification consistently benefits from the incorporation of additional graphs. We establish the mathematical foundation for the method, including the asymptotic convergence of the embedding, a sufficient condition for asymptotic optimal classification, and the proof of the synergistic effect for vertex classification. Our comprehensive simulations and real data experiments provide compelling evidence supporting the effectiveness of our proposed method, showcasing the pronounced synergistic effect for multiple graphs from disparate sources.