Account risk detection, which aims to identify accounts at forced liquidation risk within financial account-asset bipartite graphs, is crucial for ensuring financial market stability and economic resilience. Although traditional node-classification-based anomaly detection techniques can be applied to this task, these approaches often exhibit two key limitations: (1) insufficient consideration of asset fluctuations, resulting in unsatisfactory accuracy; and (2) scalability challenges, making them unsuitable for large-scale financial graphs. To address these issues, we propose RiskGuard, a novel framework for account risk detection that integrates auxiliary asset prediction and gradient-based sampling. First, we introduce an auxiliary asset prediction paradigm to capture the critical influence of asset fluctuations on account risk. Rather than solely predicting account risk, our unified model employs a Temporal-Attention Net (TANet) to jointly predict asset fluctuations and account risk. This auxiliary task enables the model to learn fluctuation-aware asset representations, significantly enhancing prediction accuracy. To overcome scalability challenges, we design GLUE, an online graph sampler leveraging gradient entropy. GLUE dynamically adjusts sampling weights based on model gradients and graph structure, prioritizing high-entropy nodes in the neighborhood for improved efficiency. Extensive experiments on five financial datasets demonstrate that RiskGuard outperforms existing techniques in accuracy while achieving high efficiency in processing large financial graphs.

Structural clustering (SCAN) is one of the most popular graph clustering paradigms, which is widely applied to understanding and analyzing the structure of social networks. SCAN assumes that the input graph is undirected and can not cluster the directed graphs. However, lots of graphs in real-world applications are directed such as financial transaction networks and citation networks. To address this problem, in this paper, we propose a new structural clustering model to cluster directed graphs. Following the new model, we propose an index-based approach to support the efficient clustering of a given graph. To further enhance the efficiency of query processing, we propose an optimized two-dimensional index and the approximate query method that achieve a speedup of up to 20× while maintaining the quality of clustering. We conduct extensive experiments on nine real directed graphs, one of which contains more than 68 million vertices and 2 billion edges. The results demonstrate the effectiveness and efficiency of our proposed methods.

Text-to-SQL has advanced rapidly with large language models, but complex database queries still require reasoning beyond one-shot generation, including multi-step decomposition, execution-based diagnosis, and targeted correction. We present EvoSQL, a co-evolution framework that formulates SQL synthesis as an iterative interaction between a generator and a critic. EvoSQL maintains a contextualized candidate memory, verifies SQL candidates with both execution signals and LLM-based critique, and updates its memory through utility-guided aggregation. To strengthen the underlying generator-critic pair, we further introduce a Self-Distillation Policy Optimization (SDPO) fine-tuning stage that injects execution-aware supervision into modern coding LLM backbones. Experiments on Spider and BIRD show that EvoSQL consistently improves open-source models over Maj@16 baselines, with particularly large gains on BIRD-Dev, ranging from +1.37

Multimodal Entity Linking (MEL) is a fundamental task in data management that maps ambiguous mentions with diverse modalities to the multimodal entities in a knowledge base. However, most existing MEL approaches primarily focus on optimizing instance-centric features and evidence, leaving broader forms of evidence and their intricate interdependencies insufficiently explored. Motivated by the observation that human expert decision-making process relies on multi-perspective judgment, in this work, we propose MSR-MEL, a Multi-perspective Evidence Synthesis and Reasoning framework with Large Language Models (LLMs) for unsupervised MEL. Specifically, we adopt a two-stage framework: (1) Offline Multi-Perspective Evidence Synthesis constructs a comprehensive set of evidence. This includes instance-centric evidence capturing the instance-centric multimodal information of mentions and entities, group-level evidence that aggregates neighborhood information, lexical evidence based on string overlap ratio, and statistical evidence based on simple summary statistics. A core contribution of our framework is the synthesis of group-level evidence, which effectively aggregates vital neighborhood information by graph. We first construct LLM-enhanced contextualized graphs. Subsequently, different modalities are jointly aligned through an asymmetric teacher-student graph neural network. (2) Online Multi-Perspective Evidence Reasoning leverages the power of LLM as a reasoning module to analyze the correlation and semantics of the multi-perspective evidence to induce an effective ranking strategy for accurate entity linking without supervision. Extensive experiments on widely used MEL benchmarks demonstrate that MSR-MEL consistently outperforms state-of-the-art unsupervised methods. The source code of this paper was available at: https://anonymous.4open.science/r/MSR-MEL-C21E/.

Community detection is a fundamental task in graph analytics that aims to identify cohesive groups of entities with similar behaviors or interests. Classic objective-driven methods struggle with complex graph structures, while deep-learning approaches improve performance at the expense of interpretability and rely on labeled data and training. Large language models (LLMs), with strong reasoning capabilities and world knowledge, are promising for interpretable, label-free community detection. To leverage these strengths, we propose LUCID, an LLM-guided, interpretable, training-free, and unsupervised community detection method. Inspired by phase-transition kinetics in natural systems, where complex structures emerge through initialization, merging, refinement, and selection, LUCID is designed as a four-stage pipeline. Within this pipeline, the LLM induces formal rules that translate implicit knowledge into explicit and interpretable logical structures. Specifically, (1) the Local-View Community Initialization stage encodes local graph structures using k-ego contexts and unsupervised node roles; (2) the Multi-factor Community Merge stage uses LLM-induced rules to iteratively merge local communities; (3) the Multi-grain Community Refinement stage applies LLM-induced coarse-to-fine rules in parallel to reduce boundary noise; and (4) the Global-view Community Selection stage identifies high-quality communities based on topological compactness and boundary clarity. Extensive experiments on real-world datasets demonstrate that LUCID, as an unsupervised approach, achieves state-of-the-art performance and consistently outperforms leading unsupervised and semi-supervised baselines.

Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become increasingly complex, different graph models have been proposed, giving rise to diverse motif patterns. These variations introduce unique computational challenges that require specialized algorithms tailored to specific motifs within different graph structures. This survey provides a comprehensive and structured overview of motif counting techniques across general graphs, heterogeneous graphs, and hypergraphs. We categorize existing algorithms according to their underlying computational strategies, emphasizing key similarities and distinctions. In addition to reviewing current methodologies, we examine their strengths, limitations, and computational trade-offs. Furthermore, we explore future directions in motif counting, including scalable implementations to improve efficiency in large-scale networks, algorithmic adaptations for dynamic, temporal, and attributed graphs, and deeper integration with large language models (LLMs) and graph-based retrieval-augmented generation (GraphRAG). By offering a detailed analysis of these approaches, this survey aims to support researchers and practitioners in advancing motif counting for increasingly complex network data.

Counting ( p , q )-bicliques in bipartite graphs is essential for uncovering dense substructures and higher-order patterns. However, releasing biclique counts can reveal private connections of users. To address this, we study ( p , q )-biclique counting under edge local differential privacy, where each vertex protects its one-hop neighbor relationships from an untrusted data curator. The Naive algorithm applies randomized responses to the adjacency matrix and produces an overly dense graph where ( p , q )-biclique structures are disrupted, resulting in highly biased estimates. To produce unbiased estimates, we propose a one-round algorithm that enumerates all motifs with p upper and q lower vertices, which leverages motif transformation probabilities to correct for perturbation-induced bias. To improve data utility and reduce the impact of Laplace noise, we propose a novel Multi-round Common Neighbor (MRCN) algorithm. MRCN estimates the number of common neighbors for each p -tuple (or q -tuple) and applies moment-based correction to recover unbiased ( p , q )-biclique counts. Notably, MRCN avoids explicit enumeration of all ( p , q )-motifs, offering better scalability for general p and q . We further boost performance with variance-reduction techniques such as multi-center optimization and refined noisy graph construction, and enhance scalability through layer-based pruning and vertex sampling. Extensive experiments on real-world datasets confirm the effectiveness and efficiency of our approaches.

Recent advances in large language models have driven the emergence of intelligent agents operating in open-world, multimodal environments. To support long-term reasoning, such agents are typically equipped with external memory systems. However, most existing multimodal agent memories rely primarily on neural representations and vector-based retrieval, which are well-suited for inductive, intuitive reasoning but fundamentally limited in supporting analytical, deductive reasoning critical for real-world decision making. To address this limitation, we propose NS-Mem, a long-term neuro-symbolic memory framework designed to advance multimodal agent reasoning by integrating neural memory with explicit symbolic structures and rules. Specifically, NS-Mem is operated around three core components of a memory system: (1) a three-layer memory architecture that consists episodic layer, semantic layer and logic rule layer, (2) a memory construction and maintenance mechanism implemented by SK-Gen that automatically consolidates structured knowledge from accumulated multimodal experiences and incrementally updates both neural representations and symbolic rules, and (3) a hybrid memory retrieval mechanism that combines similarity-based search with deterministic symbolic query functions to support structured reasoning. Experiments on real-world multimodal reasoning benchmarks demonstrate that Neural-Symbolic Memory achieves an average 4.35% improvement in overall reasoning accuracy over pure neural memory systems, with gains of up to 12.5% on constrained reasoning queries, validating the effectiveness of NS-Mem.

Bipartite graphs are commonly used to model relationships between two distinct entities in real-world applications, such as user-product interactions, user-movie ratings and collaborations between authors and publications. A butterfly (a 2x2 bi-clique) is a critical substructure in bipartite graphs, playing a significant role in tasks like community detection, fraud detection, and link prediction. As more real-world data is presented in a streaming format, efficiently counting butterflies in streaming bipartite graphs has become increasingly important. However, most existing algorithms typically assume that duplicate edges are absent, which is hard to hold in real-world graph streams, as a result, they tend to sample edges that appear multiple times, leading to inaccurate results. The only algorithm designed to handle duplicate edges is FABLE, but it suffers from significant limitations, including high variance, substantial time complexity, and memory inefficiency due to its reliance on a priority queue. To overcome these limitations, we introduce DEABC (Duplicate-Edge-Aware Butterfly Counting), an innovative method that uses bucket-based priority sampling to accurately estimate the number of butterflies, accounting for duplicate edges. Compared to existing methods, DEABC significantly reduces memory usage by storing only the essential sampled edge data while maintaining high accuracy. We provide rigorous proofs of the unbiasedness and variance bounds for DEABC, ensuring they achieve high accuracy. We compare DEABC with state-of-the-art algorithms on real-world streaming bipartite graphs. The results show that our DEABC outperforms existing methods in memory efficiency and accuracy, while also achieving significantly higher throughput.

This paper studies optical flow estimation, a critical task in motion analysis with applications in autonomous navigation, action recognition, and film production. Traditional optical flow methods require consecutive frames, which are often unavailable due to limitations in data acquisition or real-world scene disruptions. Thus, single-frame optical flow estimation is emerging in the literature. However, existing single-frame approaches suffer from two major limitations: (1) they rely on labeled training data, making them task-specific, and (2) they produce deterministic predictions, failing to capture motion uncertainty. To overcome these challenges, we propose ProbDiffFlow, a training-free framework that estimates optical flow distributions from a single image. Instead of directly predicting motion, ProbDiffFlow follows an estimation-by-synthesis paradigm: it first generates diverse plausible future frames using a diffusion-based model, then estimates motion from these synthesized samples using a pre-trained optical flow model, and finally aggregates the results into a probabilistic flow distribution. This design eliminates the need for task-specific training while capturing multiple plausible motions. Experiments on both synthetic and real-world datasets demonstrate that ProbDiffFlow achieves superior accuracy, diversity, and efficiency, outperforming existing single-image and two-frame baselines.

Hierarchical directed acyclic graph (DAG) is an essential model for representing terminologies and their hierarchical relationships, such as Disease Ontology and ImageNet categories. Due to the vast number of terminologies and complex structures in a large DAG, it becomes challenging for humans to effectively analyze and explore the hierarchical relationships they encode. Therefore, summarizing hierarchical DAGs is essential for enhancing the interpretability and visualization of the underlying hierarchy. Beyond visual data exploration, hierarchical DAG summarization also supports a range of applications, such as biomedical ontology analytics, snippet generation for information search, and summarized recommendation. In this article, we address a new problem of finding k representative vertices to summarize a hierarchical DAG. To capture diverse summarization and identify important vertices, we design a summary score function that reflects vertices diversity coverage and structure correlation. The studied problem is theoretically proven to be NP-hard. To tackle it efficiently, we propose a greedy algorithm with an approximation guarantee that iteratively adds vertices with significant summary contributions to the answers. To further enhance the answer quality, we introduce a subtree extraction-based method that is proven to achieve higher-quality answers. Additionally, we develop a scalable algorithm, k-PCGS, which employs candidate pruning and DAG compression for large-scale hierarchical DAGs. For the query-dependent problem, we propose an index-based method and several optimization techniques to improve efficiency. Extensive experiments on large real-world datasets demonstrate the effectiveness and efficiency of our proposed algorithms.

Large language models (LLMs) have been increasingly explored for graph computation, where tasks require reasoning over structured relationships and algorithmic operations. Yet, it remains unclear when LLMs can reliably support such computation and how they should be incorporated into graph-solving pipelines. Existing surveys at the intersection of LLMs and graphs primarily focus on graph learning, text-attributed graphs, or graph-language modeling. To bridge this gap, we provide a comprehensive review of LLMs for graph computation through a role-based taxonomy. Specifically, we identify two major paradigms: i) LLMs as executors, where models directly solve graph tasks from graph descriptions and instructions; and ii) LLMs as planners, where models formulate problems, decompose reasoning steps, and invoke external tools or agents for execution. Based on this taxonomy, we analyze the strengths and limitations of current methods. Our review indicates that LLMs are promising for simple, small-scale tasks, but remain unreliable for large-scale and exactness-demanding tasks. Finally, we summarize available datasets and suggest four future directions.

Data preparation is a critical step in enhancing the usability of tabular data and thus boosts downstream data-driven tasks. Traditional methods often face challenges in capturing the intricate relationships within tables and adapting to the tasks involved. Recent advances in Language Models (LMs), especially in Large Language Models (LLMs), offer new opportunities to automate and support tabular data preparation. However, why LMs suit tabular data preparation (i.e., how their capabilities match task demands) and how to use them effectively across phases still remain to be systematically explored. In this survey, we systematically analyze the role of LMs in enhancing tabular data preparation processes, focusing on four core phases: data acquisition, integration, cleaning, and transformation. For each phase, we present an integrated analysis of how LMs can be combined with other components for different preparation tasks, highlight key advancements, and outline prospective pipelines.

Effective research relies on organizing extensive information and stimulating novel solutions. Agentic systems have recently emerged as a promising tool to automate literature-based ideation. However, current systems often remain black-box. Their outputs may appear plausible but weakly grounded, with limited transparency or control for researchers. Our work introduces TrustResearcher, a multi-agent demo system for knowledge-grounded and transparent ideation. Specifically, TrustResearcher integrates meticulously designed four stages into a unified framework: (A) Structured Knowledge Curation, (B) Diversified Idea Generation, (C) Multi-stage Idea Selection, and (D) Expert Panel Review Synthesis. Different from prior pipelines, our system not only exposes intermediate reasoning states, execution logs, and tunable agents for inspections, but also enables the generation of hypotheses that are both diverse and evidence-aligned. Our design is also domain-agnostic: as long as literature sources exist, the same pipeline can be instantiated in any scientific field. As an illustrative case, we demonstrate TrustResearcher on a graph-mining case study (k-truss breaking problem), where it generates distinct, plausible hypotheses with evidence and critiques. A live demo and source code are available at https://github.com/valleysprings/TrustResearcher.

Recent studies have demonstrated the ability of Large Language Models (LLMs) in processing various graph problems. Substructure counting remains challenging in both scalability and accuracy. Incorporating sensitive edge information into the input prompts also introduces significant privacy risks of exposing the private information of user connections in real-world applications. This paper, for the first time, studies substructure counting for LLMs under edge local differential privacy (LDP) in a multi-agent framework. Unlike the Naive approach whose estimation relies entirely on overly dense noisy graphs, the proposed PSC framework decomposes substructure counting into node-level tasks distributed among node agents, and embeds the knowledge of distributed algorithms and DP frameworks in the curator agent and privacy controller, respectively. Thus, we can leverage the local neighboring information and reasoning capabilities of node agents to improve the estimation accuracy. Extensive experiments on 6 real-world datasets validate the effectiveness of PSC framework for substructure counting tasks under 𝜀 -edge LDP. Moreover, the non-DP version of PSC also demonstrated superior performance over a single LLM on standard substructure counting tasks.

In bipartite graphs, (α,β)-core is a widely used model for cohesive subgraph mining. Specifically, an (α,β)-core is a maximal subgraph in which each vertex in the upper layer has degree at least α, and each vertex in the lower layer has degree at least β. The state-of-the-art CPU-based solutions incur extensive costs to construct an index structure for all α and β combinations, leading to scalability challenges on large bipartite graphs. Moreover, on-the-fly queries, which aim to determine whether an edge update belongs to a target (α,β)-core, are essential for real-time applications such as fraud monitoring and recommendation systems. However, existing index-based methods struggle to support such queries at scale due to their high maintenance overhead. In this paper, we investigate how to leverage GPU architectures to enable efficient (α,β)-core computation and support on-the-fly queries. While GPUs are widely used to accelerate graph processing, their limited memory capacity makes it impractical to store large index structures. To address this issue, we propose GCC, an index-free GPU-based peeling algorithm that accelerates (α,β)-core computation via warp-centric processing. To further improve efficiency, we develop GCC+, which leverages the nested property of (α,β)-core with a core-based early pruning strategy. For handling on-the-fly queries, we propose GFQ, a connectivity-aware algorithm that significantly narrows the computation scope by leveraging connected component information, thereby avoiding full-graph peeling. Extensive experiments on 11 datasets demonstrate that our proposed techniques outperform existing CPU-based solutions in terms of both space and time efficiency.

The network data model can effectively capture relationships between entities, making it useful for applications such as social networks and e-commerce systems. Anomaly detection, a critical task in network analysis, focuses on identifying unusual patterns that deviate from expected behavior and plays a key role in enhancing the reliability of decision-making processes. While most existing studies focus on detecting anomalies in homogeneous networks, modern applications often involve more complex networks characterized by heterogeneity (nodes and edges of different types), diversified node attributes, and edge multiplicity (node pairs with various edges). Motivated by these practical complexities, this paper investigates anomaly detection in Attributed Multiplex Heterogeneous Networks (AMHENs), which remains challenging due to two significant gaps: the seamless integration of AMHENs’ characteristics and the comprehensive assessment of the diverse anomalies. To close these gaps, we introduce a novel Augmentation-based Multi-channel Graph convolutional network (AMG) that incorporates integrated learning and anomaly scoring mechanisms. Firstly, a multi-channel graph convolutional network is devised to capture the diverse characteristics, which can deeply learn local and global information from AMHENs and aggregate them. Secondly, to comprehensively assess varios types of anomalies, we design a hierarchical network augmentation module and an integrated model optimization module to enable the model to score anomalies through the learning of multiple views. Extensive experiments demonstrate that AMG significantly outperforms competing baselines, achieving improvements of 17.4

Bipartite graphs serve as a natural model for representing relationships between two different types of entities. When analyzing bipartite graphs, butterfly counting is a fundamental research problem that aims to count the number of butterflies (i.e., 2x2 bicliques) in a given bipartite graph. While this problem has been extensively studied in the literature, existing algorithms usually necessitate access to a large portion of the entire graph, presenting challenges in real scenarios where graphs are extremely large and I/O costs are expensive. In this paper, we study the butterfly counting problem under the query model, where the following query operations are permitted: degree query, neighbor query, and vertex-pair query. We propose TLS, a practical two-level sampling algorithm that can estimate the butterfly count accurately while accessing only a limited graph structure, achieving significantly lower query costs under the standard query model. TLS also incorporates several key techniques to control the variance, including "small-degree-first sampling" and "wedge sampling via small subsets". To ensure theoretical guarantees, we further introduce two novel techniques: "heavy-light partition" and "guess-and-prove", integrated into TLS. With these techniques, we prove that the algorithm can achieve a (1+eps) accuracy for any given approximation parameter 0 < eps < 1 on general bipartite graphs with a promised time and query complexity. In particular, the promised time is sublinear when the input graph is dense enough. Extensive experiments on 15 datasets demonstrate that TLS delivers robust estimates with up to three orders of magnitude lower query costs and runtime compared to existing solutions.

The RoboTaxi service is considered a groundbreaking mode of transportation, offering autonomous ride services to passengers. Once a travel request is placed, the passenger is picked up promptly and transported directly to their destination. Following a trip, the RoboTaxi can immediately serve another customer, remain idle, or relocate within the city to anticipate future demand. The operation of RoboTaxi systems involves two key processes: routing and rebalancing. Routing determines which vehicle will serve a passenger and in what order. Rebalancing involves moving idle vehicles to strategic locations to improve passenger satisfaction for future requests. This relies on short-term demand prediction to ensure efficient resource allocation. While existing research has primarily considered these components independently, this study integrates them into a comprehensive framework designed to improve operator profitability and passenger satisfaction. In addition, different prediction methods are adopted to examine the impact of prediction accuracy on optimization results. The results indicate that the proposed framework achieves an approximate 12 % increase in operator profits and a significant improvement in the acceptance ratio.