This state of the art was recently critiqued by O'Bray et al.

Graph perturbations are used to test robustness of algorithms. The expectation is that for small graph perturbations algorithm output should not change drastically. While graph perturbations are extensively studied in many contexts, they are underexplored for line graphs, where a line graph is an alternative representation of a graph obtained by mapping edges to vertices. But line graphs are increasingly used in many graph learning tasks including link prediction Cai et al. (2021), expressive GNNs Y ang & Huang (2024) and community detection Chen et al. (2019), and in other scientific disciplines Ruff et al. (2024), Min et al. (2023), Halldórsson et al. (2013). The reason that line graph perturbations are not commonly used is because the perturbed graph may not be a line graph. We introduce a pseudo-inverse of a line graph, which generalises the notion of the inverse line graph extending it to non-line graphs. The proposed pseudo-inverse is computed by minimally modifying the perturbed line graph so that it results in a line graph.

Graph Neural Networks (GNNs) excel at analyzing graph-structured data but struggle on heterophilic graphs, where connected nodes often belong to different classes. While this challenge is commonly addressed with specialized GNN architectures, graph rewiring remains an underexplored strategy in this context. We provide theoretical foundations linking edge homophily, GNN embedding smoothness, and node classification performance, motivating the need to enhance homophily. Building on this insight, we introduce a rewiring framework that increases graph homophily using a reference graph, with theoretical guarantees on the homophily of the rewired graph. To broaden applicability, we propose a label-driven diffusion approach for constructing a homophilic reference graph from node features and training labels. Through extensive simulations, we analyze how the homophily of both the original and reference graphs influences the rewired graph homophily and downstream GNN performance. We evaluate our method on 11 real-world heterophilic datasets and show that it outperforms existing rewiring techniques and specialized GNNs for heterophilic graphs, achieving improved node classification accuracy while remaining efficient and scalable to large graphs.

Structure learning algorithms for graphical models have focused almost exclusively on stable environments in which the underlying generative process does not change; that is, they assume that the generating model is globally stationary. In real-world environments, however, such changes often occur without warning or signal. Real-world data often come from generating models that are only locally stationary. In this paper, we present LoSST, a novel, heuristic structure learning algorithm that tracks changes in graphical model structure or parameters in a dynamic, real-time manner. We show by simulation that the algorithm performs comparably to batch-mode learning when the generating graphical structure is globally stationary, and significantly better when it is only locally stationary.

This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such property that has recently proved its utility in characterising graphs. Its expressive properties, stability, and practical utility in model evaluation remain largely unexplored, however. We combine graph curvature descriptors with emerging methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.

We study deceptive fairness attacks on graphs to answer the following question: How can we achieve poisoning attacks on a graph learning model to exacerbate the bias deceptively? We answer this question via a bi-level optimization problem and propose a meta learning-based framework named FATE. FATE is broadly applicable with respect to various fairness definitions and graph learning models, as well as arbitrary choices of manipulation operations. We further instantiate FATE to attack statistical parity and individual fairness on graph neural networks. We conduct extensive experimental evaluations on real-world datasets in the task of semi-supervised node classification. The experimental results demonstrate that FATE could amplify the bias of graph neural networks with or without fairness consideration while maintaining the utility on the downstream task. We hope this paper provides insights into the adversarial robustness of fair graph learning and can shed light on designing robust and fair graph learning in future studies.

The grounded Laplacian matrix $\LL_{-S}$ of a graph $\calG=(V,E)$ with $n=|V|$ nodes and $m=|E|$ edges is a $(n-s)\times (n-s)$ submatrix of its Laplacian matrix $\LL$, obtained from $\LL$ by deleting rows and columns corresponding to $s=|S| \ll n $ ground nodes forming set $S\subset V$. The smallest eigenvalue of $\LL_{-S}$ plays an important role in various practical scenarios, such as characterizing the convergence rate of leader-follower opinion dynamics, with a larger eigenvalue indicating faster convergence of opinion. In this paper, we study the problem of adding $k \ll n$ edges among all the nonexistent edges forming the candidate edge set $Q = (V\times V)\backslash E$, in order to maximize the smallest eigenvalue of the grounded Laplacian matrix. We show that the objective function of the combinatorial optimization problem is monotone but non-submodular. To solve the problem, we first simplify the problem by restricting the candidate edge set $Q$ to be $(S\times (V\backslash S))\backslash E$, and prove that it has the same optimal solution as the original problem, although the size of set $Q$ is reduced from $O(n^2)$ to $O(n)$. Then, we propose two greedy approximation algorithms. One is a simple greedy algorithm with an approximation ratio $(1-e^{-\alpha\gamma})/\alpha$ and time complexity $O(kn^4)$, where $\gamma$ and $\alpha$ are, respectively, submodularity ratio and curvature, whose bounds are provided for some particular cases. The other is a fast greedy algorithm without approximation guarantee, which has a running time $\tilde{O}(km)$, where $\tilde{O}(\cdot)$ suppresses the ${\rm poly} (\log n)$ factors. Numerous experiments on various real networks are performed to validate the superiority of our algorithms, in terms of effectiveness and efficiency.

Graph neural networks (GNNs) have various practical applications, such as drug discovery, recommendation engines, and chip design. However, GNNs lack transparency as they cannot provide understandable explanations for their predictions. To address this issue, counterfactual reasoning is used. The main goal is to make minimal changes to the input graph of a GNN in order to alter its prediction. While several algorithms have been proposed for counterfactual explanations of GNNs, most of them have two main drawbacks. Firstly, they only consider edge deletions as perturbations. Secondly, the counterfactual explanation models are transductive, meaning they do not generalize to unseen data. In this study, we introduce an inductive algorithm called INDUCE, which overcomes these limitations. By conducting extensive experiments on several datasets, we demonstrate that incorporating edge additions leads to better counterfactual results compared to the existing methods. Moreover, the inductive modeling approach allows INDUCE to directly predict counterfactual perturbations without requiring instance-specific training. This results in significant computational speed improvements compared to baseline methods and enables scalable counterfactual analysis for GNNs.