# Graph Convolutional Networks Guided by Explicitly Estimated Homophily and Heterophily Degree
## 4 Experiments
### Experimental Results
Let \(K\) be the number of network layers and \(L\) be the number of layers of MLP for pre-training the estimators, let \(|\mathcal{V}|\) be the number of nodes and \(|\mathcal{E}|\) be the number of edges in a graph. We also take the time cost and the numbers of parameters of FAGCN, HOG-GCN, BM-GCN and GCN-EHHD when conducting experiments on the Cora datasets as examples. Note that the time cost and the numbers of parameters of the three models for comparison are calculated according to their source code implementation. The computation complexity of a single layer in GCN-EHHD is \(\mathcal{O}(3d^{2}|\mathcal{V}|)\), and they are \(\mathcal{O}(d(|\mathcal{V}|+|\mathcal{E}|))\), \(\mathcal{O}(2d^{2}|\mathcal{V}|)\), \(\mathcal{O}(2d^{2}|\mathcal{V}|)\) for FAGCN, HOG-GCN and BM-GCN, respectively. Note that for HOG-GCN, BM-GCN and GCN-EHHD, the estimated results are calculated at the beginning of model reasoning and are used at each layer of the model. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Dataset** & **Pre-Trained \(\text{MLP}_{1}\)** & **Pre-Trained \(\text{MLP}_{2}\)** & **Fine-Tuned \(\text{MLP}_{1}\)** & **Fine-Tuned \(\text{MLP}_{2}\)** \\ \hline Cora & \(72.55\pm 1.66\) & \(80.96\pm 1.46\) & \(71.24\pm 2.81\) & \(80.74\pm 1.74\) \\ Citeseer & \(70.80\pm 2.82\) & \(61.20\pm 2.12\) & \(70.49\pm 2.71\) & \(61.03\pm 1.74\) \\ Pubmed & \(85.92\pm 0.67\) & \(82.02\pm 0.46\) & \(87.66\pm 0.72\) & \(81.45\pm 0.48\) \\ Texas & \(78.37\pm 4.93\) & \(55.40\pm 4.80\) & \(78.16\pm 5.72\) & \(51.10\pm 6.47\) \\ Wisconsin & \(84.90\pm 4.62\) & \(48.23\pm 6.00\) & \(83.68\pm 3.70\) & \(43.78\pm 7.77\) \\ Cornell & \(80.05\pm 6.67\) & \(50.81\pm 5.22\) & \(79.68\pm 3.70\) & \(46.75\pm 6.37\) \\ Chameleon & \(47.49\pm 2.63\) & \(61.27\pm 2.74\) & \(45.06\pm 2.40\) & \(61.51\pm 2.70\) \\ Squirrel & \(33.02\pm 1.38\) & \(47.58\pm 1.36\) & \(31.75\pm 1.29\) & \(48.58\pm 1.76\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Node classification accuracies of \(\text{MLP}_{1}\) and \(\text{MLP}_{2}\) of the GCN-EHHD (in % \(\pm\) Standard Error). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **Texas** & **Wisconsin** & **Squirrel** & **Chameleon** & **Cornell** \\ \hline MLP & \(78.37\pm 4.93\) & \(84.90\pm 4.62\) & \(33.02\pm 1.38\) & \(47.49\pm 2.63\) & \(80.05\pm 6.67\) \\ Deepwalk & \(55.40\pm 4.80\) & \(48.23\pm 6.00\) & \(47.58\pm 1.36\) & \(61.27\pm 2.74\) & \(50.81\pm 5.22\) \\ GCN & \(54.32\pm 8.58\) & \(46.86\pm 4.37\) & \(38.58\pm 2.02\) & \(54.97\pm 2.60\) & \(50.81\pm 7.40\) \\ GAT & \(55.67\pm 5.72\) & \(50.19\pm 4.73\) & \(40.46\pm 2.28\) & \(61.64\pm 1.30\) & \(55.94\pm 7.85\) \\ MixHop & \(71.62\pm 6.14\) & \(81.76\pm 4.98\) & \(30.22\pm 1.30\) & \(38.72\pm 2.12\) & \(72.43\pm 6.47\) \\ Geom-GCN & \(67.83\pm 4.08\) & \(64.50\pm 4.06\) & \(38.30\pm 1.05\) & \(60.72\pm 2.54\) & \(60.54\pm 3.00\) \\ FAGCN & \(72.70\pm 6.16\) & \(80.19\pm 5.58\) & \(42.82\pm 2.80\) & \(61.79\pm 4.06\) & \(71.89\pm 7.22\) \\ H2 GCN & \(78.91\pm 6.08\) & \(85.68\pm 5.31\) & \(34.63\pm 1.58\) & \(46.86\pm 2.47\) & \(79.45\pm 6.26\) \\ HOG-GCN & \(81.35\pm 5.16\) & \(84.31\pm 5.46\) & \(37.19\pm 1.54\) & \(53.59\pm 2.56\) & \(80.27\pm 6.74\) \\ BM-GCN & \(83.78\pm 6.49\) & \(77.84\pm 6.13\) & \(52.68\pm 1.79\) & \(68.85\pm 2.84\) & \(71.08\pm 6.11\) \\ \hline GCN-EHHD & \(\mathbf{87.83\pm 3.87}\) & \(\mathbf{86.27\pm 3.81}\) & \(\mathbf{54.35\pm 1.36}\) & \(\mathbf{69.32\pm 3.23}\) & \(\mathbf{81.89\pm 3.83}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Node classification accuracy on heterophilic graphs (in % \(\pm\) Standard Error). The best results are in bold, and the second-best results are underlined. The coefficients of messages must be calculated at each layer for FAGCN, and the linear transformation of features is only used in the first and the last layers in FAGCN but must be used in each layer in HOG-GCN, BM-GCN and GCN-EHHD.