This survey provides a comprehensive analysis of graph embedding techniques, their applications, and performance. Graphs, such as social networks, word co-occurrence networks, and communication networks, are prevalent in real-world applications. Analyzing these graphs helps understand societal, linguistic, and communication patterns. Recent methods using vector space representations of graph nodes have gained traction. The survey categorizes graph embedding approaches into factorization, random walk, and deep learning methods, with examples and performance analysis on various tasks. It evaluates state-of-the-art methods on common datasets and compares their performance. The survey suggests potential applications and future directions, and presents the open-source Python library GEM, which provides all discussed algorithms in a unified interface. Graph embedding techniques aim to map nodes to low-dimensional feature vectors while preserving proximity measures. Challenges include choosing the right properties to preserve, scalability, and dimensionality. The survey discusses four main tasks: node classification, link prediction, clustering, and visualization. It reviews various methods, including factorization-based approaches like LLE, Laplacian Eigenmaps, and Graph Factorization; random walk-based methods like DeepWalk and node2vec; and deep learning-based methods like SDNE and GCN. The survey also covers other methods such as HOPE and Walklets. Applications of graph embeddings include network compression, visualization, clustering, link prediction, and node classification. The survey evaluates these methods on datasets like SYN-SBM, KARATE, BLOGCATALOG, YOUTUBE, HEP-TH, ASTRO-PH, and PPI. Evaluation metrics include precision at k, mean average precision, micro-F1, and macro-F1. Results show that methods preserving higher-order proximity generally perform better. SDNE consistently performs well across datasets, while node2vec has lower reconstruction precision. HOPE and SDNE produce accurate embeddings with linear structures. The survey concludes that graph embeddings are effective for various tasks and highlights the importance of considering task-specific parameters and structures. The open-source GEM library is provided for further research.This survey provides a comprehensive analysis of graph embedding techniques, their applications, and performance. Graphs, such as social networks, word co-occurrence networks, and communication networks, are prevalent in real-world applications. Analyzing these graphs helps understand societal, linguistic, and communication patterns. Recent methods using vector space representations of graph nodes have gained traction. The survey categorizes graph embedding approaches into factorization, random walk, and deep learning methods, with examples and performance analysis on various tasks. It evaluates state-of-the-art methods on common datasets and compares their performance. The survey suggests potential applications and future directions, and presents the open-source Python library GEM, which provides all discussed algorithms in a unified interface. Graph embedding techniques aim to map nodes to low-dimensional feature vectors while preserving proximity measures. Challenges include choosing the right properties to preserve, scalability, and dimensionality. The survey discusses four main tasks: node classification, link prediction, clustering, and visualization. It reviews various methods, including factorization-based approaches like LLE, Laplacian Eigenmaps, and Graph Factorization; random walk-based methods like DeepWalk and node2vec; and deep learning-based methods like SDNE and GCN. The survey also covers other methods such as HOPE and Walklets. Applications of graph embeddings include network compression, visualization, clustering, link prediction, and node classification. The survey evaluates these methods on datasets like SYN-SBM, KARATE, BLOGCATALOG, YOUTUBE, HEP-TH, ASTRO-PH, and PPI. Evaluation metrics include precision at k, mean average precision, micro-F1, and macro-F1. Results show that methods preserving higher-order proximity generally perform better. SDNE consistently performs well across datasets, while node2vec has lower reconstruction precision. HOPE and SDNE produce accurate embeddings with linear structures. The survey concludes that graph embeddings are effective for various tasks and highlights the importance of considering task-specific parameters and structures. The open-source GEM library is provided for further research.