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Graph Neural Networks (GNNs) have received extensive research attention for their promising performance in graph machine learning. Despite their extraordinary predictive accuracy, existing approaches, such as GCN and GPRGNN, are not robust in the face of homophily changes on test graphs, rendering these models vulnerable to graph structural attacks and with limited capacity in generalizing to graphs of varied homophily levels. Although many methods have been proposed to improve the robustness of GNN models, the majority of these techniques are restricted to the spatial domain and employ complicated defense mechanisms, such as learning new graph structures or calculating edge attention. In this paper, we study the problem of designing simple and robust GNN models in the spectral domain. We propose EvenNet, a spectral GNN corresponding to an even-polynomial graph filter. Based on our theoretical analysis in both spatial and spectral domains, we demonstrate that EvenNet outperforms full-order models in generalizing across homophilic and heterophilic graphs, implying that ignoring odd-hop neighbors improves the robustness of GNNs. We conduct experiments on both synthetic and real-world datasets to demonstrate the effectiveness of EvenNet. Notably, EvenNet outperforms existing defense models against structural attacks without introducing additional computational costs and maintains competitiveness in traditional node classification tasks on homophilic and heterophilic graphs.

A.1 Prototype-based Graph Information Bottleneck - Eq. 4 From Eq. 3, the GIB objective is: min We perform ablation studies to examine the effectiveness of our model (i.e., PGIB and PGIB In Figure 7, the " with all " setting represents our final model that includes all the components. We conduct experiments on graph classification using different readout functions for PGIB. We illustrate the reasoning process on two datasets, i.e., MUT AG and BA2Motif, in Figure 8. PGIB Then, PGIB computes the "points contributed" to predicting each class by multiplying the similarity We have conducted additional qualitative analysis. It is crucial that the prototypes not only contain key structural information from the input graph but also ensure a certain level of diversity since each class is represented by multiple prototypes. Its goal is to make the masked subgraph's prediction as close as possible to the original graph, which helps to detect substructures significant

Graph-AEs are trained to capture the structural information of graphs used for training (i.e., training

Fuzzy operators can be applied to vectors of continuous values within a certain range, e.g., Different fuzzy logics implement different t-norms and t-conorms. NodePiece-QE are reported in Table 13 in Appedix D . We sampled 9 datasets (used in Section 5.2 and Section 5.3) from the original FB15k-237 [ 29 ] with Creation details are provided in the Section 5.1 and statistics on the We use those queries in Section 5.5 to Table 5: Statistics on sampled queries for each dataset ratio and query type. Furthermore, for the experiment in Section 5.3 to measure the abilities of inductive models to find Most queries (except 2i,3i) have new answer sets. Most queries have new answer sets.

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Graph Neural Networks (GNNs) have emerged as powerful models for learning from graph-structured data. However, their widespread adoption has raised serious privacy concerns. While prior research has primarily focused on edge-level privacy, a critical yet underexplored threat lies in topology privacy - the confidentiality of the graph's overall structure. In this work, we present a comprehensive study on topology privacy risks in GNNs, revealing their vulnerability to graph-level inference attacks. To this end, we propose a suite of Topology Inference Attacks (TIAs) that can reconstruct the structure of a target training graph using only black-box access to a GNN model. Our findings show that GNNs are highly susceptible to these attacks, and that existing edge-level differential privacy mechanisms are insufficient as they either fail to mitigate the risk or severely compromise model accuracy. To address this challenge, we introduce Private Graph Reconstruction (PGR), a novel defense framework designed to protect topology privacy while maintaining model accuracy. PGR is formulated as a bi-level optimization problem, where a synthetic training graph is iteratively generated using meta-gradients, and the GNN model is concurrently updated based on the evolving graph. Extensive experiments demonstrate that PGR significantly reduces topology leakage with minimal impact on model accuracy. Our code is available at https://github.com/JeffffffFu/PGR.