Real-world data are represented as graph structures in many applications that involve complex networks such as social networks, linguistic networks, biological networks, molecular drug structures, recommendation systems, and many other multimedia domain-specific data. Graph representation utilizes graph embedding techniques to convert raw graph data into high or low dimensional vectors while maintaining the intrinsic properties of graphs. With a learned graph representation, machine learning models are adopted to perform tasks whereas, deep learning models automatically learn to encode the graph structure. The choice of dimensions depends on the application domain.

The significance of graph representation is to store and access the relational knowledge of datum efficiently. Graph embedding plays a vital role in graph representation, and some of the graph embedding methods are dimensionality reduction, random walk, matrix factorization, neural networks, large graphs, hyper-graphs, and attention mechanisms.

Emerging applications of graph representation are community detection, recommendation system, node classification, link prediction, clustering, graph compression, and coarsening. Future developments of graph representation are deep graph embedding, semi-supervised graph embedding, dynamic graph embedding, scalability of graph embedding, and interpretability of graph embedding.

  • In the present decade, there is a surge in research on graph representation learning, including methods for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation.

  • Graph representation learning uses various graph embedding methods for converting the raw graph data to high-dimensional vectors and allows the relational knowledge of interacting entities to be stored and accessed efficiently.

  • However, obtaining an accurate graph representation becomes a challenging issue. It is crucial to determine the optimal embedding dimension of representation.

  • If a graph has many properties, selecting the proper graph property to embed becomes a major issue of concern.

  • Furthermore, selecting a suitable embedding method for a target application is also challenging.

  • Future research opportunities in graph embedding are Deep graph embedding, Dynamic graph embedding, Scalability of graph embedding, and Interpretability of graph embedding.

  • Owing to the ubiquitous Graph-structured data, determining the rich set of graph embedding methods in domain-specific applications is also a very challenging issue.

  • There are numerous advances in graph representation learning which have led to new state-of-the-art results in numerous domains.