# Graph Convolutional Networks Guided by Explicitly Estimated Homophily and Heterophily Degree
## 4 Experiments
### Ablation Study
For Cora, Citeseer, Pubmed, Wisconsin, Cornell and Texas, when the value of \(\alpha\) is set to be approximately \(0.5\), the performance is the best. Consider that the ablated GCN-EHHD models with \(\alpha\in\{0,1\}\) are similar, so the accuracy for \(\alpha=0\) and \(\alpha=1\) is close. For Chameleon and Squirrel, the performance is the best when \(\alpha=0\); that is, we only use negative message passing, and the performance is the worst in the vicinity of \(\alpha=0.5\). We think the difference is related to the average degree of nodes in graphs. As shown in Table 1, the average degrees of nodes in Chameleon and Squirrel are both much larger than the other datasets. For graphs with a small average degree, the influence of homophilic neighbors and heterophilic neighbors can both play important roles in message passing on heterophilic graphs. This may be the reason why the best performance is obtained in the vicinity of \(\alpha=0.5\) for Wisconsin, Cornell and Texas. Therefore, while for most graphs we can obtain a good performance by mixing positive messages with negative messages, for some heterophilic graphs with large average node degrees, it may be better to keep using negative messages alone. The analysis results of the ablation study on \(\theta\) are shown in Figures 6 and 7. For each sub-figure, the x-axis is different settings of \(\theta\), and under each setting of \(\theta\), the y-axis coordinate value of the figures on the left shows the average accuracy given the aforementioned eleven different settings of \(\alpha\). The y-axis coordinate value of the figures on the right shows the classification accuracy for \(\alpha\in\{0,0.5,1\}\), respectively. In addition, we also annotate each sub-figure with the accuracy of two pre-trained MLPs. As shown, there are three main situations. For the first situation, the better accuracy of GCN-EHHD is obtained for the values of \(\theta\) that give more importance to the pre-trained MLP with best performances on graphs such as Chameleon and Squirrel as shown in Figure 7g,h and Figure 7i,j, and Pubmed as shown in Figure 6e and Figure 6f, respectively. These three graphs are relatively large compared with other datasets. In particular, the average  
Figure 7: Analysis results of the ablation study on \(\theta\) for heterophilic graphs. The x-axis is different settings of \(\theta\). The y-axis of figures on the left shows the average accuracy under eleven different settings of \(\alpha\), and the y-axis of figures on the right shows the accuracy for \(\alpha\in\{0,0.5,1\}\), respectively. degree of nodes in Chameleon and Squirrel is quite large. For the second situation, the influence of \(\theta\) on the accuracy of GCN-EHHD is small for graphs such as Cora and Citeseer as shown in Figure 6a,b and Figure 6c,d, respectively. The difference in accuracy between the two pre-trained MLPs used for analyzing Cora and Citeseer is about 10% and not as significant as for other datasets. For the third situation, the accuracy of GCN-EHHD fluctuates with the change of \(\theta\) on graphs such as Texas, Cornell and Wisconsin as shown in Figure 7c-f and Figure 7a,b, respectively. The special performance in the third situation may mainly be because the three graphs are all relatively small which causes instability. The results indicate that the pre-trained estimator using Deepwalk is useful in measuring the homophiliy and heterophily degree on some large graphs, especially for those with large node degrees.