SIAM Review, Volume 63, Issue 4, Page 825-853, January 2021.
Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from the 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 nonlinear and highly informative graph embeddings generated 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 we present implementation details and references to open-source software as well as available databases in the supplementary material to help interested readers start their exploration into graph analytics.

中文翻译：

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理解图嵌入方法及其应用

SIAM 评论，第 63 卷，第 4 期，第 825-853 页，2021 年 1 月。
图分析可以更好地定量理解和控制复杂网络，但传统方法存在与工业规模网络的高维和异构特征相关的高计算成本和过多内存要求。图嵌入技术可以有效地将高维稀疏图转换为低维、密集和连续的向量空间，最大限度地保留图结构属性。另一种新兴的图嵌入采用基于高斯分布的图嵌入，具有重要的不确定性估计。图嵌入方法的主要目标是将每个节点的属性打包成一个更小维度的向量；因此，原始复杂不规则空间中的节点相似性可以使用标准度量在嵌入向量空间中轻松量化。在潜在空间中生成的非线性和高信息量的图嵌入可以方便地用于解决不同的下游图分析任务（例如，节点分类、链接预测、社区检测、可视化等）。在这篇综述中，我们介绍了图分析和图嵌入方法中的一些基本概念，特别关注基于随机游走和基于神经网络的方法。我们还讨论了新兴的基于深度学习的动态图嵌入方法。我们强调了图嵌入方法在四种不同应用中的独特优势，