# Graph Convolutional Networks Guided by Explicitly Estimated Homophily and Heterophily Degree
## 4 Experiments
### Experimental Results  
For all eight datasets, we adopted the test approach of [18] and randomly split the data ten times according to the division ratio \(48\%/32\%/20\%\) to generate the training/validation/test sets. We used the mean accuracy on the test set of the ten splits as the result. We report the experimental results of three homophilic graphs in Table 2, and the results of five heterophilic graphs in Table 3.  
By inspecting Tables 2 and 3, we have the following observations. On one hand, for homophilic graphs, the performances of GCN-based models under the homophily assumption were similar to that of GCN-based models tailored for dealing with heterophily. This shows that the emerging methods for tackling heterophily have good compatibility for homophily. For heterophilic graphs, these methods tailored for heterophily significantly \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Datasets** & **Nodes** & **Edges** & **Features** & **Classes** & \(\mathbf{d_{avg}}\) & \(\mathbf{h}\) \\ \hline Texas & 183 & 309 & 1703 & 5 & 1.68 & 0.09 \\ Wisconsin & 251 & 499 & 1703 & 5 & 1.98 & 0.19 \\ Squirrel & 5201 & 198,493 & 2089 & 5 & 38.16 & 0.22 \\ Chameleon & 2277 & 31,421 & 2325 & 5 & 13.79 & 0.23 \\ Cornell & 183 & 309 & 1703 & 5 & 1.68 & 0.30 \\ Citeseer & 3327 & 4732 & 3703 & 6 & 1.42 & 0.74 \\ Pubmed & 19,717 & 44,338 & 500 & 3 & 2.24 & 0.80 \\ Cora & 2708 & 5429 & 1433 & 7 & 2.00 & 0.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of datasets. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **Cora** & **Citeseer** & **Pubmed** \\ \hline MLP & \(72.55\pm 1.66\) & \(70.80\pm 2.82\) & \(85.92\pm 0.67\) \\ Deepwalk & \(80.96\pm 1.46\) & \(61.20\pm 2.12\) & \(82.02\pm 0.46\) \\ GCN & \(86.53\pm 1.51\) & \(75.00\pm 2.12\) & \(87.31\pm 0.73\) \\ GAT & \(86.70\pm 1.28\) & \(74.95\pm 2.46\) & \(86.42\pm 0.81\) \\ MixHop & \(86.65\pm 1.62\) & \(74.12\pm 1.64\) & \(89.09\pm 0.60\) \\ Geom-GCN & \(85.05\pm 1.50\) & \(75.16\pm 1.57\) & \(88.07\pm 0.56\) \\ FAGCN & \(87.10\pm 1.81\) & \(75.77\pm 1.43\) & \(88.67\pm 0.67\) \\ H2 GCN & \(85.39\pm 1.14\) & \(73.72\pm 1.95\) & \(84.25\pm 0.61\) \\ HOG-GCN & \(86.01\pm 1.44\) & \(75.25\pm 2.37\) & \(88.50\pm 0.61\) \\ BM-GCN & \(\mathbf{87.60\pm 1.32}\) & \(76.17\pm 1.49\) & \(89.32\pm 0.76\) \\ \hline GCN-EHHD & \(87.20\pm 1.36\) & \(\mathbf{76.34\pm 1.86}\) & \(\mathbf{90.01\pm 0.60}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Node classification accuracy on homophilic graphs (in % \(\pm\) Standard Error). The best results are in bold, and the second-best results are underlined. outperformed traditional GCNs. On the other hand, for homophilic graphs, our GCN-EHHD outperformed all the baselines on Citeseer and Pubmed and achieved the second best on Cora. For heterophilic graphs, GCN-EHHD outperformed all the baselines on the five datasets. Especially, GCN-EHHD achieved 4.83%, 3.17% and 2.01% improvement on Texas, Squirrel and Cornell, respectively. Therefore, our proposed model can achieve the best or comparable performance on both homophilic and heterophilic graphs. The accuracies of \(\text{MLP}_{1}\) and \(\text{MLP}_{2}\) of the GCN-EHHD are also meaningful for analyzing the performance of GCN-EHHD. We show the accuracies of pre-trained \(\text{MLP}_{1}\), \(\text{MLP}_{2}\) and final \(\text{MLP}_{1}\), \(\text{MLP}_{2}\) after fine-tuning in Table 4. In our experiments, in general, the better the MLPs accuracies were, the better the accuracy of the whole GCN-EHHDwas, especially for the large graph. We discuss the effect of pre-trained estimators in Section 4.4. Next, we discuss the computation complexity and model complexity compared with three representative and competitive models, including FAGCN, HOG-GCN and BM-GCN. To facilitate comparison, we assume that for each model, the dimensions of the input layer, the output layer and all hidden layers are equal and denoted by \(d\).