  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.
