# Graph Convolutional Networks Guided by Explicitly Estimated Homophily and Heterophily Degree
## 4 Experiments
### Ablation Study  
In order to explore the role of negative message passing guided by heterophily degree and estimator generated by Deepwalk, we conducted an ablation study. Recall that the hyperparameter \(\alpha\) in Equation (14) controls the proportion of aggregated positive and negative messages from the neighbors, and the hyperparameter \(\theta\) in Equation (9) controls the  
Figure 3: The visualization of the output embedding of the last layer in GCN, FAGCN, BM-GCN and GCN-EHHD on the Chameleon dataset by t-SNE with nodes colored according to their class labels. proportion of node attributes and graph structure information when estimating homophily degree and heterophily degree. We therefore perform an ablation study by comparing different settings of parameters \(\alpha\) and \(\theta\), and report their effects on the predictive accuracy of node classification tasks. We chose eleven values of \(\alpha\) in the interval \([0,1]\). When \(\alpha=1\), it amounts to discarding the part of negative message passing and only aggregating positive messages from neighbors. When \(\alpha=0\), the reverse is true. For each setting of \(\alpha\), we chose eleven values of \(\theta\) ranging from 0 to 1. When \(\theta=0\), we only used the pre-trained estimator generated based on graph structure information extracted by Deepwalk. When \(\theta=1\), we only considered node attributes for estimating the homophily and heterophily degree. For each setting of \(\alpha\) and \(\theta\), we conducted node classification experiments as described in Section 4.2 on the aforementioned eight datasets in Section 4.1 and report the experimental results as given in Figures 4-7. Figure 4: Analysis results of the ablation study on \(\alpha\) for homophilic graphs. The x-axis is different settings of \(\alpha\). The y-axis of figures on the left shows the average accuracy under eleven different settings of \(\theta\), and the y-axis of figures on the right shows the accuracy for \(\theta\in\{0.05,1\}\), respectively. Figure 5: Cont. Figure 5: Analysis results of the ablation study on \(\alpha\) for heterophilic graphs. The x-axis is different settings of \(\alpha\). The y-axis of figures on the left shows the average accuracy under eleven different settings of \(\theta\), and the y-axis of figures on the right shows the accuracy for \(\theta\in\{0,0.5,1\}\), respectively. Figure 6: Analysis results of the ablation study on \(\theta\) for homophilic 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. Figure 7: _Cont._  
The analysis results of the ablation study on \(\alpha\) are shown in Figures 4 and 5. For each sub-figure, the x-axis is different settings of \(\alpha\), and under each setting of \(\alpha\), the y-axis coordinate value of the figures on the left shows the average accuracy given the aforementioned eleven different settings of \(\theta\), and the y-axis coordinate value of the figures on the right shows the classification accuracy for \(\theta\in\{0,0.5,1\}\), respectively. As shown, there are three main situations. For the first situation, the influence of \(\alpha\) on the model accuracy in average is small for graphs such as Cora, Citeseer and Pubmed. For the second situation, the plots are characterized by sort of \"reverse U-shape\", where the accuracy values for \(\alpha=0\) and \(\alpha=1\) are close to each other, and the best results are obtained in the vicinity of \(\alpha=0.5\). The analysis results for Wisconsin, Cornell and Texas are this case. In the third situation, the plots for Chameleon and Squirrel are characterized by sort of \"U-shape\". When \(\alpha=1\), that is, the negative message passing is cancelled, the performance is not the best in the eight datasets, and in particular is poor on Cornell, Wisconsin and Texas. This validates the effectiveness of negative message passing.