# Graph Convolutional Networks Guided by Explicitly Estimated Homophily and Heterophily Degree
## 4 Experiments  
### Experimental Settings  
**Datasets.** We chose eight widely-adopted datasets. Following [26], we used the homophily ratio \(h=\frac{|(u,v);(u,v)\in\mathcal{E}\wedge y_{u}=v_{v}|}{|\mathcal{E}|}\) to describe the homophily level for a graph. We chose three homophilic graph datasets: Cora, Citeseer and Pubmed [31; 32], and five heterophilic graph datasets: Texas, Wisconsin, Squirrel, Chameleon and Cornell [18]. The statistics of these datasets are listed in Table 1, where \(h\) represents the homophily ratio of a graph, and \(d_{avg}=\frac{|\mathcal{E}|}{|\mathcal{V}|}\) represents the average degree of nodes in a graph.  
**Baseline Methods.** We compared our proposed model with the following baselines: (1) MLP which only uses original node attributes information; (2) Deepwalk [24] which only uses graph topology information; (3) GCN-based models under the assumption of homophily: GCN [1] and GAT [2]; and (4) GCN-based models that deal with heterophilic graphs: MixHop [19], Geom-GCN [18], FAGCN [20], H2 GCN [26], HOG-GCN [22] and BM-GCN [23].  
**Implementation.** The baselines MLP and Deepwalk were the same methods with the MLP\({}_{1}\) and MLP\({}_{2}\) in GCN-EHHD, respectively, and the parameter settings and training procedures of baselines MLP and Deepwalk were the same as those of the pre-trained MLP\({}_{1}\) and MLP\({}_{2}\) in GCN-EHHD, respectively. For GCN and GAT, the dimension of hidden layers was set as 64, the number of layers was set as 2, the Adam optimizer [33] was used as optimizer, the learning rate was set as 0.001, and the weight decay was set as 5E-4. The number of attention heads in GAT was set as five. The number of training epochs of GCN and GAT was set as 1600 with the early stopping strategy of 100 patience epochs. For other baselines, the optimal parameters and the training procedures were taken as reported in their original papers. We implemented our proposed GCN-EHHD based on PyTorch [34]. We utilized the Adam optimizer [33] to train the GCN-EHHD. In the process of generating embedding \(\mathbf{X}^{E}\) using Deepwalk, the number of random walk generators was set as 80, the maximum length of random walk was set as 10, and the windows size was set as 5. For each dataset, the embedding dimension of \(\mathbf{X}^{E}\) was the same as the original features \(\mathbf{X}\). For both the MLP module and the GCN module, the number of layers was searched in \(\{2,3\}\), and the dimension of hidden layer was searched in \(\{32,64\}\). The learning rate was set in \(\{0.001,\,0.005\}\), and the weight decay was set in \(\{0.02,\,5\text{E-}4,\,5\text{E-}5\}\). For different datasets, The parameter \(\delta\) in Equation (11) for controlling the contribution of self-loops was set in \(\{0,\,1,2\}\), the hyperparameter \(\alpha\) in Equation (14) was set in \(\{0,\,0.4,\,0.5\}\), and the hyperparameter \(\theta\) in Equation (9) was set in \(\{0.1,\,0.4,\,0.6,\,1\}\). The impact of the parameter \(\alpha\) and \(\theta\) is analyzed in Section 4.4. To train GCN-EHHD, the number of pre-training epochs was set as 400, the number of jointly training epochs was set as 1600 with the early stopping strategy with 100 patience epochs following the training procedure of [23].