Keywords: Graph structured data, Graph representations, Graph-based neural networks, Graph embedding, Graph Convolutions.

1 Introduction  
1.1 Contribution  
1.2 Graph Data Domains  

2 Graph Theory  
2.1 Concepts  
2.2 Matrix Representation of Graphs  

3 Use Cases  
3.1 Graph Comparison  
3.2 Graph Classification  
3.3 Link Prediction  
3.4 Graph Clustering  
3.5 Further Use Cases  

4 Kernel Methods  
4.1 Kernels Methods for Graphs  

5 Learning Graph Representations  
5.1 Kernel Approaches  
5.2 Convolution Approaches  
5.3 Graph Neural Networks  
5.4 Graph Embedding Approaches  
5.5 Probabilistic Approaches  

6 Future Directions