This paper surveys the state-of-the-art works on network embedding and points out future research directions. It categorizes network embedding methods into three types: structure and property preserving, network embedding with side information, and advanced information preserving. The paper discusses the motivation for network embedding, traditional graph embedding methods, and the differences between graph embedding and network embedding. It reviews various network embedding methods, including those that preserve network structures, properties, and side information. The paper also presents evaluation scenarios and online resources for network embedding. It concludes with a discussion of future research directions. Network embedding aims to represent network nodes in a low-dimensional space, preserving network structure and properties. It has applications in network analysis tasks such as node classification, clustering, visualization, and link prediction. Network embedding can support these tasks more efficiently than traditional network representation methods. The paper highlights the importance of preserving network structures and properties in network embedding, as well as the role of side information in enhancing the performance of network embedding methods. It also discusses the challenges of network embedding, including high computational complexity, low parallelizability, and inapplicability of machine learning methods. The paper concludes that network embedding is a promising approach for network representation and analysis, with potential for future research and applications.This paper surveys the state-of-the-art works on network embedding and points out future research directions. It categorizes network embedding methods into three types: structure and property preserving, network embedding with side information, and advanced information preserving. The paper discusses the motivation for network embedding, traditional graph embedding methods, and the differences between graph embedding and network embedding. It reviews various network embedding methods, including those that preserve network structures, properties, and side information. The paper also presents evaluation scenarios and online resources for network embedding. It concludes with a discussion of future research directions. Network embedding aims to represent network nodes in a low-dimensional space, preserving network structure and properties. It has applications in network analysis tasks such as node classification, clustering, visualization, and link prediction. Network embedding can support these tasks more efficiently than traditional network representation methods. The paper highlights the importance of preserving network structures and properties in network embedding, as well as the role of side information in enhancing the performance of network embedding methods. It also discusses the challenges of network embedding, including high computational complexity, low parallelizability, and inapplicability of machine learning methods. The paper concludes that network embedding is a promising approach for network representation and analysis, with potential for future research and applications.