Thank you for your appreciated feedback. Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.

Q1

Justification: Our model is designed to separately process graph signals with different levels of homophily. Specifically, we use $AX$ to extract homophilic signals, $IX$ to obtain full-pass signals, and $LX$ to capture heterophilic signals. Furthermore, this design aligns with our theoretical analysis, which shows that the entire model can be optimized by minimizing the distributional shifts of ${D_{\text{KL}}(A^S X^S | A^T X^T)}$, ${D_{\text{KL}}(X^S | X^T)}$, and ${D_{\text{KL}}(L^S X^S | L^T X^T)}$.

Laplacian matrix $L$: Regarding $L$, There might be some misunderstanding. In fact, the graph Laplacian matrix can be viewed as a high-pass filter that obtains heterophilic signals—a perspective that has been adopted in several existing works [1, 2, 3] (e.g., in Section2.1 of [1], it says "To address the heterophily challenge, high-pass(HP) filter $L$ is often used to replace low-pass(LP) filter $A$"). To the best of our knowledge, we are unaware of any graph theory that contradicts utilizing a Laplacian matrix to obtain heterophilic signals. We are pleased to provide more clarification and havea more detailed discussion with you regarding this matter if you still have concerns.

[1] Luan S, Hua C, Xu M, et al. When do graph neural networks help with node classification? Investigating the homophily principle on node distinguishability. Advances in Neural Information Processing Systems, 2023.

[2] Luan S, Hua C, Lu Q, et al. Revisiting heterophily for graph neural networks. Advances in neural information processing systems, 2022.

[3] Li B, Pan E, Kang Z. Pc-conv: Unifying homophily and heterophily with two-fold filtering. Proceedings of the AAAI conference on artificial intelligence. 2024.

Q2

Thanks for your constructive comment! Following your suggestion, we also conducted additional experiments, evaluating MAG using macro-F1 and Twitch using AUC to address your concern. Due to word limitations, we have provided visualizations of these tables in the supplementary material, accessible via the following link MAG and Twitch.

Q3

We acknowledge the importance of comparing our approach with recent advancements, including TDSS, A2GNN, GraphAlign [1*,2*,3*]. We report the performance of HGDA and the baseline methods on the Airport, ACM, Blog and Citation datasets. For the results on MAG and Twitch, please refer to our response to Q2. Our results demonstrate that while their method performs well, our approach exhibits outperformance, highlighting the importance of minimizing homophily shift. In future version, we will include these baseline methods along with additional evaluation metrics.

Q4

Thank you for your valuable comment. We believe there might be a slight misunderstanding regarding the notion of "enhancing graph homophily" in the context of our work. Our paper does not aim to improve or increase the inherent homophily of the graph itself. Instead, our focus is on highlighting the homophily shift that occurs between the source and target domains in graph domain adaptation (GDA), and proposing a method to mitigate this shift. We will further revise our paper to clarify this point. Regarding the justification on this point, we provide experimental results that report the classification accuracy on target graph subgroups with varying levels of homophily. The results show that $HGDA_L$ performs best in subgroups with high homophily, $HGDA_F$ performs best in subgroups with intermediate homophily, and $HGDA_H$ performs best in subgroups with low homophily. These findings underscore the effectiveness of our method, which employs a combination of filters to mitigate homophily discrepancies at various levels.

Q5

Regarding the concern about $Z_L$, $Z_F$, and $Z_H$, we would like to clarify that these embeddings are obtained by applying homophilic, full-pass, and heterophilic filters, respectively. In Table 1, Table 2, and Table 3, the variants $HGDA_L$, $HGDA_F$, and $HGDA_H$ exclusively utilize $Z_L$, $Z_F$, and $Z_H$, respectively. The results of the main experiments show that each variant performs differently across datasets, which we attribute to the intrinsic homophily distribution characteristics of each dataset. The effects of $Z_L$, $Z_F$, and $Z_H$ are further demonstrated by the experiments discussed in Q4.

For clarification, the GCN baseline under the standard unsupervised GDA setting employs a two-layer GCN architecture combined with an MMD loss for domain alignment.

Thank you for your constructive feedback! Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.

Q1

Thanks for your constructive comment! Following your suggestion, we also conducted additional experiments, evaluating HGDA performance on ogbn-arxiv dataset. Specifically, we report the performance of HGDA on three tasks. As for ogbn-arxivl networks, we choose the year to separate networks, which are collected from 1950-2016(50-16), 2016-2018(16-18), and 2018-2020(18-20). As for Twitch RU and ES, we are pleased to provide their experiment, which is as follows link. Our results demonstrate that while their method performs well, our approach exhibits outperformance, highlighting the importance of minimizing homophily shift. In future versions, we will include these baseline methods along with additional evaluation metrics.

Q2

We apologize for any misunderstanding caused by the previous lack of clarity. To clarify, overall graph node homophily ratio is $\; \int_{0}^{1} v \,\cdot\, H^v_{\text{node}} \,\mathrm{d}v.$

which actually is our Definition 1 (Graph-Level Node Heterophily Distribution) in Section3.3. This method computes the homophily distribution across the entire graph. As shown in Fig. 1, in the Airport dataset, while the overall graph-level node heterophily distributions of the BRAZIL and EUROPE subgraphs are relatively similar, significant differences exist in the local homophily subgroups. These observations highlight the need for our model to handle homophily shifts effectively at different levels.

Q3

To address your concern, we provide experimental results that report the classification accuracy on target graph subgroups with varying levels of homophily. We also provide synthetic experiments to validate the effectiveness of our three filter pairs in addressing varying levels of homophily shift, which detail can be found in Reviewer BNmW in Q4. The results show that $HGDA_L$ performs best in subgroups with high homophily, $HGDA_F$ performs best in subgroups with intermediate homophily, and $HGDA_H$ performs best in subgroups with low homophily. These findings support the effectiveness of our method in aligning graph signals across different levels of homophily. Therefore, we can conclude that these three modules provide different roles in HGDA.

Q4

Regarding Definition 1 (Graph-Level Node Heterophily Distribution), $P_G^H$ captures structural information inherent to the graph, as observed in nature [1, 2]. Consequently, unless the graph topology itself is directly altered, $P_G^H$​ remains a fixed quantity. As a result, ${D_{\text{KL}}(P_S^H \| P_T^H)}$ is also an intrinsic and fixed value. Following your suggestion, we will address these concerns and provide clarification in a future version of the paper.

[1] Pan E, Kang Z. Beyond homophily: Reconstructing structure for graph-agnostic clustering. International conference on machine learning. , 2023.

[2] Xie X, Chen W, Kang Z. Robust graph structure learning under heterophily. Neural Networks, 2025.

Thank you for your comment regarding Table line problems. We apologize for this and have carefully reviewed and corrected them throughout the paper in the future version.

Thank you for your feedback. We would also appreciate your agreement on our method's novelty and effectiveness. Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.

Q1

$KL(Z_L^S \| Z_L^T)$ aligns the homophilic signal, corresponding to the term $D_{\text{KL}}(A^S X^S \| A^T X^T)$. Similarly, $KL(Z_H^S \| Z_H^T)$ directly aligns the graph attributes, corresponding to the term $D_{\text{KL}}(X^S \| X^T)$. Finally, $KL(Z_F^S \| Z_F^T)$ aligns the heterophilic signal, which is consistent with the term $D_{\text{KL}}(L^S X^S \| L^T X^T)$ in Theorem 1. Specifically, this can be explained as follows. The term ${D_{\text{KL}}(A^S X^S | A^T X^T)}$ quantifies the divergence in the graph homophily signal, capturing how graph attributes—modulated by the adjacency matrices—differ between the source and target graphs. In contrast, ${D_{\text{KL}}(X^S | X^T)}$ measures the divergence in the distribution of graph attributes between the two domains. Lastly, ${D_{\text{KL}}(L^S X^S | L^T X^T)}$ quantifies the divergence in the graph heterophilic signal, where the attributes are modulated by the graph Laplacian matrix.

Q2

Some early works have addressed graph homogeneity through reconstruction [1] to enhance graph homophily, our work does not directly modify the graph structure due to the computational complexity involved. Instead, our method focuses on processing homophilic information at varying levels by grouping nodes accordingly. Inspired by theoretical insights, the model employs low-pass, full-pass, and high-pass filters to capture homophilic signals at different levels. We are pleased to discuss these topics in the related work section of the future version.

[1] Pan E, Kang Z. Beyond homophily: Reconstructing structure for graph-agnostic clustering. International conference on machine learning. , 2023.

Q3

Thanks for your constructive comment! Following your suggestion, we also conducted additional experiments, evaluating HGDA performance on ogbn-arxiv dataset. Specifically, we report the performance of HGDA on three tasks. As for ogbn-arxiv networks, we choose years to separate networks, which are collected from 1950- 2016 (50- 16), 2016- 2018 (16- 18), and 2018- 2020 (18- 20). Our results demonstrate that while their method performs well, our approach exhibits outperformance, highlighting the importance of minimizing homophily shift. We will include these baseline methods and additional evaluation metrics in future versions.

Thank you for your comment regarding typo problems. We apologize for this and have carefully reviewed and corrected them throughout the paper in the future version.

Thank you for your feedback. We would also appreciate your agreement on our method's novelty and effectiveness. Below, we address the concerns and questions raised in the Claims And Evidence, Weaknesses, Theoretical Claims, and Questions For Authors section. Please feel free to reach out if further clarification is required.

Q1

As shown in Fig. 5, HGDA achieves balanced performance across different subgroups by processing graph signals with varying levels of homophily through three specialized filters. Specifically, $HGDA_L$ performs well in homophilic subgroups, $HGDA_H$ excels in heterophilic subgroups, and $HGDA_F$ is most effective in subgroups with intermediate homophily levels. The combined contributions of these components lead to an overall balanced performance.

Q2

1. We acknowledge that continued research into graph-structured data will further enhance the effectiveness of such approaches. However, HGDA method incorporates both homophilic and heterophilic filters that leverage the structural information of the graph.

2. Our motivation is to address subgroups with varying levels of homophily. To this end, we employ a homophilic filter to extract subgroups with high homophily, a full-pass filter for those with middle homophily, and a heterophilic filter for subgroups with low homophily [1]. This behavior can be observed in Fig. 5. As stated in Theorem 1, ${D_{\text{KL}}(P_S^H | P_T^H)}$ cannot be directly optimized as shown in Definition1. However, we can instead minimize the divergence of different homophily-level signals by optimizing ${D_{\text{KL}}(A^S X^S | A^T X^T)}$, ${D_{\text{KL}}(X^S | X^T)}$, and ${D_{\text{KL}}(L^S X^S | L^T X^T)}$, thereby alleviating homophily divergence.

3. In this paper, we focus on addressing the challenge of homophily shift. We acknowledge that covariate shift, label shift, and particularly conditional structure shift are also critical issues related to homophily in graph domain adaptation (GDA), which we plan to explore in future work.

Q2

As noted in Appendix B, each experiment was repeated five times, and the reported results represent the average performance. Additionally, we will include the standard deviation of the results in future versions of the paper.

Q3

The key difference between $HGDA_F$ and DANN lies in their alignment strategies: $HGDA_F$ employs a KL divergence-based alignment loss, whereas DANN uses an adversarial loss. Moreover, DANN does not incorporate the pseudo-label classification loss on the target graph, which is included in our approach. These differences likely account for the performance gap observed between the two methods. Overall, the performance of different HGDA variants is related to the underlying distribution of the dataset. Specifically, in this experiment, $HGDA_L$ and $HGDA_F$ tend to perform better on datasets with a higher proportion of homophilic subgroups, while $HGDA_H$ and $HGDA_F$ perform better on datasets with a relatively higher degree of heterophily. In the meanwhile, we really appreciate your question, which gives us the opportunity to further improve our manuscript. Specifically, in light of your comments, we will revise Section 5.3 to further clarify our motivation and avoid potential confusion.

Q4

We provide synthetic experiments to validate the effectiveness of our three filter pairs in addressing varying levels of homophily shift. Specifically, we randomly generated five sets of source and target graphs, each containing 300 nodes, where the homophily properties for each subgroup were varied in increments of 0.01. In the picture, the horizontal axis denotes the various homophily subgroups of target graphs, and the vertical axis indicates the performance of different HGDA variants across these homophily levels. The results indicate that $HGDA_L$ performs best in high-homophily scenarios, $HGDA_F$ excels in medium-homophily settings, and $HGDA_H$ is most effective in low-homophily contexts.

Q5

We would like to further clarify that, as demonstrated in Theorem 1, the performance differences between source and target domain adaptation are influenced not only by component $\sqrt{D_{\text{KL}}(P_S^F \| P_T^F)}$, but also by component $L^\gamma_S(\phi)$. Moreover, the effectiveness of $L^\gamma_S(\phi)$ across different adaptation tasks also depends on the source domain's empirical risk, which indicates an accuracy gap between two adaptation directions.

Q6

The use of KL divergence in our loss function is theoretically motivated. Additionally, incorporating these three loss terms does not significantly increase computational overhead. The overall computational complexity of HGDA remains controlled at $O(N^2 \cdot d)$.