The diffusion model with multiple conditions has received widespread attention in the field of drug design due to its high-quality generation ability. However, the paradigm of directly generating new molecules from conditions used in existing work has not accurately fitted the joint distribution of multiple conditions during the generation process. To address this issue, we propose Graph Diffusion Evolution Model(GDEM) for multi conditional molecule generation. GDEM decomposes the process of molecular generation into a chain-like Markov evolution process, continuously adjusting the molecular structure and gradually approaching the true multi-conditional joint distribution. Meanwhile, in order to effectively train this chain evolution generative model, we also propose a two-stage training approximation method to complete the training of intermediate steps. We validated the effectiveness of GDEM on multiple polymer datasets and small molecule datasets, and the results showed that GDEM has advantages in molecular properties and condition control compared to traditional methods.
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Bipartite graphs are widely used to model relationships between entities of different types, where vertices are divided into two disjoint sets. Biclique-preserving clustering is a fundamental operation that retrieves clusters with dense bicliques, enabling various emerging applications. However, existing methods either fail to accurately capture the unique properties of bipartite graphs or significantly overlook the informative higher-order biclique substructure, leading to compromised clustering quality. Additionally, existing methods are overly dependent on biclique enumeration, resulting in poor scalability. To address these challenges, we propose ECRC, a simple yet provable Edge-Centric Reweighting Clustering framework that provides strict approximation guarantees for any biclique. A key advantage of ECRC is its ability to leverage powerful counting instead of exhaustive enumeration, significantly reducing time and space complexity. To further improve efficiency, we propose several effective graph reduction strategies to eliminate the unqualified vertices and edges before calculating the edge-centric weight. Extensive experiments on five datasets show that our algorithms are more efficient and effective compared to six baselines.
The ''pre-train, prompt'' paradigm, designed to bridge the gap between pre-training tasks and downstream objectives, has been extended from the NLP domain to the graph domain and has achieved remarkable progress. Current mainstream graph prompt-tuning methods modify input or output features using learnable prompt vectors. However, existing approaches are confined to single-granularity (e.g., node-level or subgraph-level) during prompt generation, overlooking the inherently multi-scale structural information in graph data, which limits the diversity of prompt semantics. To address this issue, we pioneer the integration of multi-scale information into graph prompt and propose a Multi-Scale Graph Chain-of-Thought (MSGCOT) prompting framework. Specifically, we design a lightweight, low-rank coarsening network to efficiently capture multi-scale structural features as hierarchical basis vectors for prompt generation. Subsequently, mimicking human cognition from coarse-to-fine granularity, we dynamically integrate multi-scale information at each reasoning step, forming a progressive coarse-to-fine prompt chain. Extensive experiments on eight benchmark datasets demonstrate that MSGCOT outperforms the state-of-the-art single-granularity graph prompt-tuning method, particularly in few-shot scenarios, showcasing superior performance. The code is available at: https://github.com/zhengziyu77/MSGCOT.
Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based γ-quasi-clique model offers a flexible alternative by identifying subgraphs whose edge densities exceed a specified threshold γ. However, finding the exact maximum edge-based quasi-clique is computationally challenging, as the problem is NP-hard and lacks the hereditary property. These characteristics limit the effectiveness of conventional pruning methods and the development of efficient reduction rules. As a result, existing algorithms, such as QClique and FPCE, struggle to scale to large graphs. In this paper, we revisit the problem and propose a novel iterative framework that reformulates the problem as a sequence of hereditary subproblems, enabling more effective pruning and reduction strategies and improving the worst-case time complexity. Furthermore, we redesign the iterative process and introduce a novel heuristic to further improve practical efficiency. Extensive experiments on 253 large-scale real-world graphs demonstrate that our proposed algorithm EQC-Pro outperforms existing methods by up to four orders of magnitude.
Graph anomaly detection (GAD) identifies nodes, edges, and subgraphs that deviate from normal patterns, playing a key role in cybersecurity, finance, and web technologies. However, existing deep learning paradigms trained on fixed datasets struggle to generalize to unseen graphs, while current graph foundation models (GFMs) face inherent challenges in anomaly detection. Their generalization objectives conflict with the rarity and divergence of anomalies, and existing attempts to develop GFMs for GAD mainly fall into two directions: single-task cross-domain models and domain-specific multi-task models. The former transfers knowledge across domains but fails to capture cross-level dependencies, whereas the latter handles multiple tasks jointly but lacks cross-domain adaptability. Both rely heavily on labeled data, limiting scalability. These limitations highlight the need for a unified unsupervised graph foundation model capable of generalizing across domains and detecting anomalies at multiple levels. We propose GFM-UAD, a Graph Foundation Model for Unified Anomaly Detection. It is pretrained on a single dataset and performs multi-level anomaly detection across unlabeled domains. To address anomaly scarcity, GFM-UAD extracts high-confidence normal samples and synthesizes diverse anomalies through adversarial generation. By freezing the backbone and fine-tuning the detection head with distribution alignment and message passing, the model adapts flexibly to unseen environments without supervision. Experiments across multiple datasets demonstrate that GFM-UAD achieves superior accuracy and generalization, establishing a foundation for future unsupervised graph foundation models in anomaly detection.
In this paper, we propose Graph Retention Networks (GRNs) as a unified architecture for deep learning on dynamic graphs. The GRN extends the concept of retention into dynamic graph data as graph retention, equipping the model with three key computational paradigms: parallelizable training, low-cost O(1) inference, and long-term chunkwise training. This architecture achieves an optimal balance between efficiency, effectiveness, and scalability. Extensive experiments on benchmark datasets demonstrate its strong performance in both edge-level prediction and node-level classification tasks with significantly reduced training latency, lower GPU memory overhead, and improved inference throughput by up to 86.7x compared to SOTA baselines. The proposed GRN architecture achieves competitive performance across diverse dynamic graph benchmarks, demonstrating its adaptability to a wide range of tasks.
In web-based systems, elements are commonly organized within a graph structure, with each node collecting essential spatio-temporal data. Examples include websites on the World Wide Web, traffic monitors in transportation networks, or sensors in the Internet of Things (IoT). However, sensors are typically deployed sparsely and unevenly, leaving the remaining nodes unobserved. The spatio-temporal kriging task, which infers values at unobserved nodes from observed ones, has thus attracted significant research interest. Due to limitations such as reliance on static graph structures and iterative Graph Convolution Network (GCN) frameworks, accurate kriging remains challenging. To address these issues, we propose a Diffusion-based Kriging Model with Graph-enhanced Attention (DKM-GA). Our approach first introduces a graph-enhanced attention mechanism that dynamically learns more accurate graph structures by combining predefined graph knowledge with global node value similarities. It is then integrated into a diffusion-based framework, which is tailored for the reliance of attention on known values. Therefore, the framework progressively refines the target values using correlated nodes, and the graph-enhanced attention selects more relevant neighbors based on the refined values. Furthermore, a node-based rescaling strategy is introduced to align the inference phase graphs to the training ones. Experiments on eight real-world datasets demonstrate that DKM-GA achieves superior performance, reducing estimation errors by up to 12.66%. Moreover, our analysis identifies three practical scenarios where the model delivers greater performance gains, even achieving 19.51% improvements on datasets that show minor gains under standard settings. These results highlight the effectiveness and potential of our model, while the scenarios provide settings for more comprehensive evaluations in terms of performance and robustness.
Real-world temporal graphs are largely driven by sequential dynamics, and edge repetitions are rare. This characteristic has spotlighted a key limitation of existing temporal graph neural networks (T-GNNs): on such graphs, state-of-the-art T-GNNs often achieve less than 70% MRR on link prediction. Two factors drive this shortfall: (1) Memory modules and neighbor co-occurrence encodings in existing T-GNNs often fail since they rely on memorizing exact neighbor identities and on the co-occurrence assumption. (2) Existing T-GNNs are sensitive to abrupt events, which are common in sequential settings that can exceed ten million updates, thereby compromising generalization. To tackle the challenges of sequential dynamics, we propose SeqFilter, a simple yet robust neural network that functions as a composite filter for link prediction on temporal graphs. SeqFilter comprises two modules: a node rhythm memory and a frequency-selective structure encoder. The node rhythm memory shifts the focus from who interacts to when, modeling absolute timestamps with recency awareness to capture each node's interaction rhythm. To model temporal structures in complex sequential dynamics, we propose a frequency-selective structure encoder that amplifies or suppresses specific frequencies in the neighbor spectrum, enabling the effective modeling of local structure correlations. Theoretically, this encoder functions as a cascade of three learnable filters that approximate the optimal linear denoiser, helping capture the underlying structural patterns. Last, SeqFilter fuses the outputs of two modules to generate high-quality node embeddings. Extensive experiments across eight sequential dynamic datasets show that SeqFilter outperforms 11 baselines by an average improvement of 15.82% in MRR while achieving an order of magnitude speedup compared to the frequency-enhanced baseline.
Recently, Graph Foundation Models (GFMs) have emerged as a central focus in the field of graph learning due to their strong generalizability to various unseen graphs. However, existing GFMs typically work under the homophily assumption, and the exploration of universality on heterophilic graphs is still in its early stages. In fact, even in homophilic graphs, there exists limited yet informative heterophilic information that is not fully exploited by current GFMs. Moreover, due to the requirement for universality, the heterophily issue faced by GFMs is more challenging than in classical graph learning, as it requires training a single model to adapt to varying structures, features, and tasks. Classic heterophilic graph learning methods primarily based on the node-level homophily or heterophily. However, we highlight that homophily and heterophily exist not only at the node semantic level, but also at a finer granularity across individual feature dimensions. This finding enables GFMs to adapt to heterophilic graphs and better utilize the small amount of heterophilic information in homophilic graphs. Based on this, we propose Topology-aware Feature Sorting Graph Foundation Model (TFSGFM), which employs a feature-level topology-aware sorting strategy and a dual-channel graph neural network framework, enabling unified modeling of both feature and structure. Extensive experiments demonstrate the strong generalizability of TFSGFM. The source code is available at https://github.com/hedongxiao-tju/TFSGFM.
Liquid Time-Constant networks (LTCs), a type of continuous-time graph neural network, excel at modeling irregularly-sampled dynamics but are fundamentally confined to Euclidean space. This limitation introduces significant geometric distortion when representing real-world graphs with inherent non-Euclidean structures (e.g., hierarchies and cycles), degrading representation quality. To overcome this limitation, we introduce the Riemannian Liquid Spatio-Temporal Graph Network (RLSTG), a framework that unifies continuous-time liquid dynamics with the geometric inductive biases of Riemannian manifolds. RLSTG models graph evolution through an Ordinary Differential Equation (ODE) formulated directly on a curved manifold, enabling it to faithfully capture the intrinsic geometry of both structurally static and dynamic spatio-temporal graphs. Moreover, we provide rigorous theoretical guarantees for RLSTG, extending stability theorems of LTCs to the Riemannian domain and quantifying its expressive power via state trajectory analysis. Extensive experiments on real-world benchmarks demonstrate that, by combining advanced temporal dynamics with a Riemannian spatial representation, RLSTG achieves superior performance on graphs with complex structures. Project Page: https://rlstg.github.io
Graph incremental learning aims to sequentially adapt models to evolving graphs while mitigating catastrophic forgetting. This problem becomes particularly challenging due to the simultaneous occurrence of covariate and label distribution shifts, introduced by newly emerging node classes, changes in node feature styles, and additional edges. To address these challenges, we propose DINGLE, a novel framework for both class and domain (class-domain) incremental learning on graphs. DINGLE consists of two key modules: a representation decoupler, which disentangles node representations into domain-invariant semantic factors for classification and domain-specific variation factors, and a teacher-student knowledge distillation module, which facilitates knowledge transfer across tasks while mitigating catastrophic forgetting through memory replay. By leveraging a Representative Node Feature (RNF) bank and an Encoder Parameters (EP) bank, DINGLE ensures effective knowledge retention and adaptation. Extensive experiments on 5 real-world datasets demonstrate that DINGLE outperforms 11 state-of-the-art baselines in class-domain incremental learning, improving classification accuracy while effectively preventing forgetting across tasks.
Unsupervised graph domain adaptation (UGDA) aims to transfer knowledge from a labeled source graph to an unlabeled target graph, addressing the performance degradation caused by distributional shifts in node attributes and graph structures across domains. Despite recent progress, existing UGDA approaches still face two key challenges: (C1) Data-level: Most methods rely on a single source domain, overlooking the complementary knowledge that could be leveraged from multiple sources. (C2) Model-level: Many UGDA models emphasize complex, handcrafted Graph neural network (GNN) architectures, while simpler yet effective designs with propagation (P) & transformation (T) pipeline remain underexplored. To address these challenges, in this paper, we propose a novel approach, which leverages Concise Propagation–Transformation pipeline for multi-source unsupervised Graph Domain Adaptation, dubbed as CPT-GDA, to better capture complementary knowledge from multiple sources in an efficient manner. Specifically, the proposed CPT-GDA adopts a dual-branch GNN architecture with different depths of propagation but the same P-T patterns, which enables the model to efficiently learn node representations to mitigate domain discrepancy. Meanwhile, to facilitate effective knowledge transfer across graphs, we derive three optimization objectives: (1) the classifier loss to learn discriminative representations; (2) the alignment loss weighted by the graph Wasserstein distance to align the structure and feature distribution; and (3) the pseudo-label loss to refine target node representations. Extensive experiments on real-world datasets confirm that the proposed method outperforms recent state-of-the-art baselines, demonstrating its effectiveness.
The remarkable success of large language models (LLMs) has motivated researchers to adapt them as universal predictors for various graph-related tasks, with the ultimate goal of developing a graph foundation model that generalizes diverse scenarios. The key challenge is to align graph data with language spaces so that LLMs can better comprehend graphs. As a popular paradigm, Graph-Tokenizing LLMs (GTokenLLMs) encode complex structures and lengthy texts into a graph token sequence, and then align them with text tokens via language instructions tuning. Despite their initial success, our information-theoretic analysis reveals that existing GTokenLLMs rely solely on text supervision from language instructions, which achieve only implicit graph–text alignment, resulting in a text-dominant bias that underutilizes graph context. To overcome this limitation, we first prove that the alignment objective is upper-bounded by the mutual information between the input graphs and their hidden representations in the LLM, which motivates us to improve this upper bound to achieve better alignment. To this end, we further propose a reconstructive graph instruction tuning pipeline, RGLM. Our key idea is to reconstruct the graph information from the LLM's graph token outputs, explicitly incorporating graph supervision to constrain the alignment process. Technically, we embody RGLM by exploring three distinct variants from two complementary perspectives: RGLM-Decoder from the input space; RGLM-Similarizer and RGLM-Denoiser from the latent space. Additionally, we theoretically analyze the alignment effectiveness of each variant. Extensive experiments on various benchmarks and task scenarios validate the effectiveness of the proposed RGLM, paving the way for new directions in GTokenLLMs' alignment research.
Graph rationalization methods aim to improve the explainability of Graph Neural Networks by identifying critical subgraphs (rationales) for task prediction. Motivated by increasing concerns over data privacy, federated graph rationalization has recently gained traction as a novel research area. However, in federated settings, data heterogeneity across clients exacerbates shortcut learning, where models rely on spurious and client-specific features rather than invariant causal rationales. Existing solutions, such as environment-aware data augmentation, suffer from low-quality environment representations. To address this, we propose DiffGR, a Diff erence-based sample selection strategy for federated Graph Rationalization. DiffGR selects samples where local and global models exhibit the highest prediction discrepancies, as these likely reflect strong shortcut reliance, enabling more accurate environment representations. Additionally, we introduce a mutual information (MI) inspired environment-conditioned data augmentation method that minimizes MI between environments and predictions while maximizing MI between rationales and predictions. Experiments on real-world and synthetic datasets demonstrate the effectiveness of DiffGR in improving rationale quality and model robustness in federated settings. Code is available at https://github.com/yuelinan/Codes-of-DiffGR.
Digital labor markets are increasingly used to procure diverse forms of human input, from data annotation to food delivery. A central concern in such markets is the ability of platforms to suppress wages by exploiting the abundance of low-cost labor. To better understand labor outcomes, we introduce a novel posted-price procurement model with coverage objectives. In our model a platform seeks to acquire a set of M tasks while minimizing wait time, as well as total spending. Workers are sampled from a population and complete a task if the posted price is higher than their estimated cost of labor. First, we show that with a simple pricing strategy the platform can cover all categories in time O(M), while paying only a O(log(M)/M) fraction of the total cost of labor by exploiting high worker uncertainty about their costs. Then, we study the impact of collective action to prevent the exploitation of workers. We show how a small, strategically chosen coalition of workers that commits to a price floor forces the platform's total spending from logarithmic to linear in M, substantially reducing the power of the platform to suppress wages. In contrast, a randomly sampled coalition of equal size remains largely ineffective. We complement our theory with synthetic experiments that demonstrate the benefit of targeted recruitment for collective action across different market regimes. More broadly, our results provide a theoretical foundation for understanding how to organize collective bargaining for promoting welfare in digital labor markets.
Online market platforms play an increasingly powerful role in the economy. An empirical phenomenon is that platforms, such as Amazon, Apple, and DoorDash, also enter their own marketplaces, imitating successful products developed by third-party sellers. We formulate a Stackelberg model, where the platform acts as the leader by committing to an entry policy: when will it enter and compete on a product? We study this model through a theoretical and computational framework. We begin with a single seller, and consider different kinds of policies for entry. We characterize the seller's optimal explore-exploit strategy via a Gittins-index policy, and give an algorithm to compute the platform's optimal entry policy. We then consider multiple sellers, to account for competition and information spillover. Here, the Gittins-index characterization fails, and we employ deep reinforcement learning to examine seller equilibrium behavior. Our findings highlight the incentives that drive platform entry and seller innovation, consistent with empirical evidence from markets such as Amazon and Google Play, with implications for regulatory efforts to preserve innovation and market diversity.
We initiate the study of single-sample bilateral trade with a broker, drawing an analogy to the setting of single-sample bilateral trade without a broker considered in [1] and [5]. Our model captures the three-sided interaction in which a broker mediates trade between a buyer and seller, each described by a valuation distribution from which a single sample can be drawn. We consider two settings in particular: one where the valuation distributions of the buyer and seller are identical and one where the valuation distributions are stochastically ordered. We analyze simple mechanisms that rely only on a single sample from each agent's distribution and show that these mechanisms achieve constant-factor approximations to the first-best gains-from-trade (GFT), first-best social welfare (SW), and optimal profit under the standard monotone-hazard-rate assumption. We then complement these results with matching or nearly matching upper bounds on the GFT and SW of our mechanisms. Notably, in both settings, we observe fairly small losses in the approximation factors to the first-best GFT and first-best SW due to the existence of the broker (benchmarked against the corresponding approximation factors in the setting without a broker). Furthermore, our results stand in stark contrast to those of [12], who show inapproximability results under a strategic broker with full distributional knowledge. Our results provide insight into the design of data-efficient brokerage mechanisms for online marketplaces and decentralized trading platforms, where intermediaries must facilitate trade under severe informational constraints. They highlight how even minimal data can enable robust and incentive-compatible brokerage in uncertain markets for both the broker and the market participants.
Data powers almost everything we experience on the web today---from the recommendations and ads we see to the AI systems and online marketplaces that shape our digital interactions. The increasing demand for high-quality data has given rise to platforms that facilitate the buying and selling of data. A key practical challenge in such markets is determining how to price data. Competitive equilibrium (CE), a foundational concept in classical market economics, determines prices for rivalrous goods by matching their supply and demand. In this work, we initiate the study of CE in data markets, explicitly incorporating the role of data in improving predictive performance in buyers' utility functions, and the non-rival nature of data by adapting the standard market-clearing condition to allow the simultaneous allocation of data records to multiple buyers. We analyze the existence, structure, and computation of CE in such data markets. We establish that CE always exists, and almost all instances admit a unique and rational equilibrium price vector. In general, however, there could be a non-convex set of prices, which rules out convex-programming approaches for finding a CE. Despite these challenges, we design an FPTAS for computing approximate equilibria using a Walrasian-style price adjustment algorithm. Our framework opens avenues for studying richer buyer utilities under correlated data sellers, and deeper structural and algorithmic aspects of data markets.