# Understanding graph embedding methods and their applications

arXiv: https://arxiv.org/abs/2012.08019 · HTML: https://mlsanity.com/paper/2012.08019/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2020.

## Built on by (most cited first, 30 of 51)

- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Scalable algorithms for physics-informed neural and graph networks](https://mlsanity.com/paper/2205.08332/) (2022)
- [GraphInsight: Unlocking Insights in Large Language Models for Graph Structure Understanding](https://mlsanity.com/paper/2409.03258/) (2024)
- [TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers](https://mlsanity.com/paper/2307.02588/) (2023)
- [DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs](https://mlsanity.com/paper/2109.13441/) (2021)
- [Topological Node2vec: Enhanced Graph Embedding via Persistent Homology](https://mlsanity.com/paper/2309.08241/) (2023)
- [Hyperdimensional Representation Learning for Node Classification and Link Prediction](https://mlsanity.com/paper/2402.17073/) (2024)
- [DNNAbacus: Toward Accurate Computational Cost Prediction for Deep Neural Networks](https://mlsanity.com/paper/2205.12095/) (2022)
- [A Comprehensive Survey on Graph Summarization with Graph Neural Networks](https://mlsanity.com/paper/2302.06114/) (2023)
- [Machine Learning on Dynamic Graphs: A Survey on Applications](https://mlsanity.com/paper/2401.08147/) (2024)
- [An embedding-based distance for temporal graphs](https://mlsanity.com/paper/2401.12843/) (2024)
- [GRVFL-MV: Graph Random Vector Functional Link Based on Multi-View Learning](https://mlsanity.com/paper/2409.04743/) (2024)
- [Hierarchical Retrieval: The Geometry and a Pretrain-Finetune Recipe](https://mlsanity.com/paper/2509.16411/) (2025)
- [Robustness of shallow graph embedding methods for community detection](https://mlsanity.com/paper/2405.00636/) (2024)
- [Knowledge-aware Document Summarization: A Survey of Knowledge, Embedding Methods and Architectures](https://mlsanity.com/paper/2204.11190/) (2022)
- [Hub-aware Random Walk Graph Embedding Methods for Classification](https://mlsanity.com/paper/2209.07603/) (2022)
- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [Bounded Projection Matrix Approximation with Applications to Community Detection](https://mlsanity.com/paper/2305.15430/) (2023)
- [TPM: Transition Probability Matrix -- Graph Structural Feature based Embedding](https://mlsanity.com/paper/2208.03712/) (2022)
- [Reliable Malware Analysis and Detection using Topology Data Analysis](https://mlsanity.com/paper/2211.01535/) (2022)
- [Graph Embedding Augmented Skill Rating System](https://mlsanity.com/paper/2304.08257/) (2023)
- [Improving embedding of graphs with missing data by soft manifolds](https://mlsanity.com/paper/2311.17598/) (2023)
- [One for All and All for One: GNN-based Control-Flow Attestation for Embedded Devices](https://mlsanity.com/paper/2403.07465/) (2024)
- [Efficient Graph Encoder Embedding for Large Sparse Graphs in Python](https://mlsanity.com/paper/2406.03726/) (2024)
- [TopER: Topological Embeddings in Graph Representation Learning](https://mlsanity.com/paper/2410.01778/) (2024)
- [An unified approach to link prediction in collaboration networks](https://mlsanity.com/paper/2411.01066/) (2024)
- [Learning Time-Varying Graph Signals via Koopman](https://mlsanity.com/paper/2511.06493/) (2025)
- [An Impossibility Theorem for Node Embedding](https://mlsanity.com/paper/2105.13251/) (2021)
- [Fast Computation of Generalized Eigenvectors for Manifold Graph Embedding](https://mlsanity.com/paper/2112.07862/) (2021)

## Abstract (arXiv)

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and heterogeneous characteristics of industrial size networks. Graph embedding techniques can be effective in converting high-dimensional sparse graphs into low-dimensional, dense and continuous vector spaces, preserving maximally the graph structure properties. Another type of emerging graph embedding employs Gaussian distribution-based graph embedding with important uncertainty estimation. The main goal of graph embedding methods is to pack every node's properties into a vector with a smaller dimension, hence, node similarity in the original complex irregular spaces can be easily quantified in the embedded vector spaces using standard metrics. The generated nonlinear and highly informative graph embeddings in the latent space can be conveniently used to address different downstream graph analytics tasks (e.g., node classification, link prediction, community detection, visualization, etc.). In this Review, we present some fundamental concepts in graph analytics and graph embedding methods, focusing in particular on random walk-based and neural network-based methods. We also discuss the emerging deep learning-based dynamic graph embedding methods. We highlight the distinct advantages of graph embedding methods in four diverse applications, and present implementation details and references to open-source software as well as available databases in the Appendix for the interested readers to start their exploration into graph analytics.