1 Introduction  
2 Preliminary of Graphs  
3 Network Motifs  
3.1 Foundation and Algorithms  
3.2 Use Cases and Applications  
4 Simplicial Complexes  
4.1 Foundation and Algorithms  
4.2 Use Cases and Applications  
5 Hypergraphs  
5.1 Foundation and Algorithms  
5.2 Use Cases and Applications  
6 Datasets and Tools  
6.1 Higher-Order Network Tools  
6.2 Higher-Order Datasets  
6.3 Expected Time Complexities  
7 Conclusions and Future Directions  
7.1 Data Source and Modeling  
7.2 Machine Learning Applications