## 3 Route Planning Scheme Based on Scatter-GNN
### Problem Definition
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **ACC** & **Macro-F** \\ \hline DeepWalk & 47.6003 & 43.0754 \\ Node2 vec & 48.4542 & 45.2780 \\ GCN & 57.35 \(\pm\) 1.4 & 54.02 \(\pm\) 1.2 \\ Scatter-GCN & 57.49 \(\pm\) 1.3 & 54.05 \(\pm\) 1.2 \\ GAT & 60.21 \(\pm\) 1.4 & 58.18 \(\pm\) 1.6 \\ Scatter-GAT & 60.24 \(\pm\) 1.5 & 58.20 \(\pm\) 1.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation on edge graph link prediction (%) using GNN as the base model. Figure 5: Line existence probability statistics. planning schemes. Nevertheless, it shows some improvement in accuracy compared with the GAT model. With the continuous increase in high-speed railway lines in China, the adjacent stations of each station continue to increase, and the prediction of the Scatter-GNN model is more accurate. It can not only assist manual line selection in actual line planning, ease the burden of investigation, but also re-evaluate existing operating lines. In the end, it can be applied to other routing scenarios such as roads, flight lines, etc. This is also likely to become a new way of thinking for future research on line planning, design, construction, and other similar issues. At the same time, the Scatter-GNN model also has the following limitations in practical applications:

1. Since the Scatter-GNN model needs to constantly judge whether to add sites and routes before formal training, this makes it less efficient than traditional GNN classifiers;
2. Due to the extremely limited number of railway stations, the prediction accuracy of the graph deep learning model is not high;
3. The adaptive function defined in the Scatter-GNN model is based on the assumption \(n\rightarrow\infty\). However, the stations in the railway line network eventually become saturated, which limits the model prediction performance. In view of the above deficiencies, this paper intends to focus on the following issues in future research:

1. How to divide the scope of the adaptive function more carefully, so as to further improve the prediction performance of the model;
2. Explore ways to limit the number of potential neighbor sites to improve prediction efficiency. These will be a meaningful challenges for future research. Conceptualization, M.M. ; methodology, M.M. and Y.Z. ; software, M.M. and Y.Z. ; validation, Y.Z. ; formal analysis, M.M. and Y.Z. ; investigation, M.M. ; resources, M.M. ; data curation, M.M. ; writing--original draft preparation, M.M. and Y.Z. ; writing--review and editing, M.M., Y.Z. and Y.L. ([PERSON]); supervision, M.M. and Y.Z. ; project administration, X.L. and Y.L. ([PERSON]); funding acquisition, Y.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China (Grant no. 72161034, 61863032) and The Major Scientific Research Projects of Northwest Normal University (Grant no. NWNU-LKZD2021-06). Not applicable. The authors declare no conflict of interest. ## Appendix A

In Section 3.1, this paper makes the following statement on the input data requirements of the Scatter-GNN model:

1. The input datasets in the model are all structured data, which should be a graph data structure. For example, transportation network, Weibo social network, urban population map, epidemic transmission network, and terrain structure map, etc. They should all conform to the definition of graph: Graph = (V,E). Among them, node V represents a city, an individual, and a website. The edge E represents the relationship between them, such as the social relationship between known people, the existing route between roads or railways, the mutual concern between two sites, etc. If there is only a set of nodes but no edges, it does not meet the input requirements of the model. It should be noted that the existing set of connected edges should have practical significance. 2. The acceptable data format for the model is: tabular form (excel) or adjacency matrix form.