Daily Papers

Subgraph matching is a fundamental building block for graph-based applications and is challenging due to its high-order combinatorial nature. Existing studies usually tackle it by combinatorial optimization or learning-based methods. However, they suffer from exponential computational costs or searching the matching without theoretical guarantees. In this paper, we develop D2Match by leveraging the efficiency of Deep learning and Degeneracy for subgraph matching. More specifically, we first prove that subgraph matching can degenerate to subtree matching, and subsequently is equivalent to finding a perfect matching on a bipartite graph. We can then yield an implementation of linear time complexity by the built-in tree-structured aggregation mechanism on graph neural networks. Moreover, circle structures and node attributes can be easily incorporated in D2Match to boost the matching performance. Finally, we conduct extensive experiments to show the superior performance of our D2Match and confirm that our D2Match indeed exploits the subtrees and differs from existing GNNs-based subgraph matching methods that depend on memorizing the data distribution divergence

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of k-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

Fine-tuning pre-trained language models (PLMs) has recently shown a potential to improve knowledge graph completion (KGC). However, most PLM-based methods focus solely on encoding textual information, neglecting the long-tailed nature of knowledge graphs and their various topological structures, e.g., subgraphs, shortest paths, and degrees. We claim that this is a major obstacle to achieving higher accuracy of PLMs for KGC. To this end, we propose a Subgraph-Aware Training framework for KGC (SATKGC) with two ideas: (i) subgraph-aware mini-batching to encourage hard negative sampling and to mitigate an imbalance in the frequency of entity occurrences during training, and (ii) new contrastive learning to focus more on harder in-batch negative triples and harder positive triples in terms of the structural properties of the knowledge graph. To the best of our knowledge, this is the first study to comprehensively incorporate the structural inductive bias of the knowledge graph into fine-tuning PLMs. Extensive experiments on three KGC benchmarks demonstrate the superiority of SATKGC. Our code is available.

Federated Learning (FL) on graphs enables collaborative model training to enhance performance without compromising the privacy of each client. However, existing methods often overlook the mutable nature of graph data, which frequently introduces new nodes and leads to shifts in label distribution. Since they focus solely on performing well on each client's local data, they are prone to overfitting to their local distributions (i.e., local overfitting), which hinders their ability to generalize to unseen data with diverse label distributions. In contrast, our proposed method, FedLoG, effectively tackles this issue by mitigating local overfitting. Our model generates global synthetic data by condensing the reliable information from each class representation and its structural information across clients. Using these synthetic data as a training set, we alleviate the local overfitting problem by adaptively generalizing the absent knowledge within each local dataset. This enhances the generalization capabilities of local models, enabling them to handle unseen data effectively. Our model outperforms baselines in our proposed experimental settings, which are designed to measure generalization power to unseen data in practical scenarios. Our code is available at https://github.com/sung-won-kim/FedLoG

Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests refactoring them into a unified design space for graph matching networks. Existing methods occupy only a few isolated patches in this space, which remains largely uncharted. We undertake the first comprehensive exploration of this space, featuring such axes as attention-based vs. soft permutation-based interaction between query and corpus graphs, aligning nodes vs. edges, and the form of the final scoring network that integrates neural representations of the graphs. Our extensive experiments reveal that judicious and hitherto-unexplored combinations of choices in this space lead to large performance benefits. Beyond better performance, our study uncovers valuable insights and establishes general design principles for neural graph representation and interaction, which may be of wider interest.

Graph-based retrieval-augmented generation (Graph RAG) is increasingly deployed to support LLM applications by augmenting user queries with structured knowledge retrieved from a knowledge graph. While Graph RAG improves relational reasoning, it introduces a largely understudied threat: adversaries can reconstruct subgraphs from a target RAG system's knowledge graph, enabling privacy inference and replication of curated knowledge assets. We show that existing attacks are largely ineffective against Graph RAG even with simple prompt-based safeguards, because these attacks expose explicit exfiltration intent and are therefore easily suppressed by lightweight safe prompts. We identify three technical challenges for practical Graph RAG extraction under realistic safeguards and introduce GRASP, a closed-box, multi-turn subgraph reconstruction attack. GRASP (i) reframes extraction as a context-processing task, (ii) enforces format-compliant, instance-grounded outputs via per-record identifiers to reduce hallucinations and preserve relational details, and (iii) diversifies goal-driven attack queries using a momentum-aware scheduler to operate within strict query budgets. Across two real-world knowledge graphs, four safety-aligned LLMs, and multiple Graph RAG frameworks, GRASP attains the strongest type-faithful reconstruction where prior methods fail, reaching up to 82.9 F1. We further evaluate defenses and propose two lightweight mitigations that substantially reduce reconstruction fidelity without utility loss.

Subgraph representation learning is a technique for analyzing local structures (or shapes) within complex networks. Enabled by recent developments in scalable Graph Neural Networks (GNNs), this approach encodes relational information at a subgroup level (multiple connected nodes) rather than at a node level of abstraction. We posit that certain domain applications, such as anti-money laundering (AML), are inherently subgraph problems and mainstream graph techniques have been operating at a suboptimal level of abstraction. This is due in part to the scarcity of annotated datasets of real-world size and complexity, as well as the lack of software tools for managing subgraph GNN workflows at scale. To enable work in fundamental algorithms as well as domain applications in AML and beyond, we introduce Elliptic2, a large graph dataset containing 122K labeled subgraphs of Bitcoin clusters within a background graph consisting of 49M node clusters and 196M edge transactions. The dataset provides subgraphs known to be linked to illicit activity for learning the set of "shapes" that money laundering exhibits in cryptocurrency and accurately classifying new criminal activity. Along with the dataset we share our graph techniques, software tooling, promising early experimental results, and new domain insights already gleaned from this approach. Taken together, we find immediate practical value in this approach and the potential for a new standard in anti-money laundering and forensic analytics in cryptocurrencies and other financial networks.

Subgraph-based graph representation learning (SGRL) has recently emerged as a powerful tool in many prediction tasks on graphs due to its advantages in model expressiveness and generalization ability. Most previous SGRL models face computational challenges associated with the high cost of subgraph extraction for each training or test query. Recently, SUREL was proposed to accelerate SGRL, which samples random walks offline and joins these walks online as a proxy of subgraph for representation learning. Thanks to the reusability of sampled walks across different queries, SUREL achieves state-of-the-art performance in terms of scalability and prediction accuracy. However, SUREL still suffers from high computational overhead caused by node duplication in sampled walks. In this work, we propose a novel framework SUREL+ that upgrades SUREL by using node sets instead of walks to represent subgraphs. This set-based representation eliminates repeated nodes by definition but can also be irregular in size. To address this issue, we design a customized sparse data structure to efficiently store and access node sets and provide a specialized operator to join them in parallel batches. SUREL+ is modularized to support multiple types of set samplers, structural features, and neural encoders to complement the structural information loss after the reduction from walks to sets. Extensive experiments have been performed to validate SUREL+ in the prediction tasks of links, relation types, and higher-order patterns. SUREL+ achieves 3-11times speedups of SUREL while maintaining comparable or even better prediction performance; compared to other SGRL baselines, SUREL+ achieves sim20times speedups and significantly improves the prediction accuracy.

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science applications such as link, relation and motif prediction. However, current SGRL approaches suffer from scalability issues since they require extracting subgraphs for each training or test query. Recent solutions that scale up canonical GNNs may not apply to SGRL. Here, we propose a novel framework SUREL for scalable SGRL by co-designing the learning algorithm and its system support. SUREL adopts walk-based decomposition of subgraphs and reuses the walks to form subgraphs, which substantially reduces the redundancy of subgraph extraction and supports parallel computation. Experiments over six homogeneous, heterogeneous and higher-order graphs with millions of nodes and edges demonstrate the effectiveness and scalability of SUREL. In particular, compared to SGRL baselines, SUREL achieves 10times speed-up with comparable or even better prediction performance; while compared to canonical GNNs, SUREL achieves 50% prediction accuracy improvement.

Subgraphs of a larger global graph may be distributed across multiple devices, and only locally accessible due to privacy restrictions, although there may be links between subgraphs. Recently proposed subgraph Federated Learning (FL) methods deal with those missing links across local subgraphs while distributively training Graph Neural Networks (GNNs) on them. However, they have overlooked the inevitable heterogeneity between subgraphs comprising different communities of a global graph, consequently collapsing the incompatible knowledge from local GNN models. To this end, we introduce a new subgraph FL problem, personalized subgraph FL, which focuses on the joint improvement of the interrelated local GNNs rather than learning a single global model, and propose a novel framework, FEDerated Personalized sUBgraph learning (FED-PUB), to tackle it. Since the server cannot access the subgraph in each client, FED-PUB utilizes functional embeddings of the local GNNs using random graphs as inputs to compute similarities between them, and use the similarities to perform weighted averaging for server-side aggregation. Further, it learns a personalized sparse mask at each client to select and update only the subgraph-relevant subset of the aggregated parameters. We validate our FED-PUB for its subgraph FL performance on six datasets, considering both non-overlapping and overlapping subgraphs, on which it significantly outperforms relevant baselines. Our code is available at https://github.com/JinheonBaek/FED-PUB.

Automatic extraction of chemical structures from scientific literature plays a crucial role in accelerating research across fields ranging from drug discovery to materials science. Patent documents, in particular, contain molecular information in visual form, which is often inaccessible through traditional text-based searches. In this work, we introduce SubGrapher, a method for the visual fingerprinting of chemical structure images. Unlike conventional Optical Chemical Structure Recognition (OCSR) models that attempt to reconstruct full molecular graphs, SubGrapher focuses on extracting molecular fingerprints directly from chemical structure images. Using learning-based instance segmentation, SubGrapher identifies functional groups and carbon backbones, constructing a substructure-based fingerprint that enables chemical structure retrieval. Our approach is evaluated against state-of-the-art OCSR and fingerprinting methods, demonstrating superior retrieval performance and robustness across diverse molecular depictions. The dataset, models, and code are publicly available.

We present a novel edge-level ego-network encoding for learning on graphs that can boost Message Passing Graph Neural Networks (MP-GNNs) by providing additional node and edge features or extending message-passing formats. The proposed encoding is sufficient to distinguish Strongly Regular Graphs, a family of challenging 3-WL equivalent graphs. We show theoretically that such encoding is more expressive than node-based sub-graph MP-GNNs. In an empirical evaluation on four benchmarks with 10 graph datasets, our results match or improve previous baselines on expressivity, graph classification, graph regression, and proximity tasks -- while reducing memory usage by 18.1x in certain real-world settings.

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which SSWL achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. Furthermore, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that SSWL-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

To deduce new facts on a knowledge graph (KG), a link predictor learns from the graph structure and collects local evidence to find the answer to a given query. However, existing methods suffer from a severe scalability problem due to the utilization of the whole KG for prediction, which hinders their promise on large scale KGs and cannot be directly addressed by vanilla sampling methods. In this work, we propose the one-shot-subgraph link prediction to achieve efficient and adaptive prediction. The design principle is that, instead of directly acting on the whole KG, the prediction procedure is decoupled into two steps, i.e., (i) extracting only one subgraph according to the query and (ii) predicting on this single, query dependent subgraph. We reveal that the non-parametric and computation-efficient heuristics Personalized PageRank (PPR) can effectively identify the potential answers and supporting evidence. With efficient subgraph-based prediction, we further introduce the automated searching of the optimal configurations in both data and model spaces. Empirically, we achieve promoted efficiency and leading performances on five large-scale benchmarks. The code is publicly available at: https://github.com/tmlr-group/one-shot-subgraph.

Recent advancements in large language models (LLMs) have shown impressive versatility across various tasks. To eliminate its hallucinations, retrieval-augmented generation (RAG) has emerged as a powerful approach, leveraging external knowledge sources like knowledge graphs (KGs). In this paper, we study the task of KG-driven RAG and propose a novel Similar Graph Enhanced Retrieval-Augmented Generation (SimGRAG) method. It effectively addresses the challenge of aligning query texts and KG structures through a two-stage process: (1) query-to-pattern, which uses an LLM to transform queries into a desired graph pattern, and (2) pattern-to-subgraph, which quantifies the alignment between the pattern and candidate subgraphs using a graph semantic distance (GSD) metric. We also develop an optimized retrieval algorithm that efficiently identifies the top-k subgraphs within 1-second latency on a 10-million-scale KG. Extensive experiments show that SimGRAG outperforms state-of-the-art KG-driven RAG methods in both question answering and fact verification, offering superior plug-and-play usability and scalability.

Graph retrieval based on subgraph isomorphism has several real-world applications such as scene graph retrieval, molecular fingerprint detection and circuit design. Roy et al. [35] proposed IsoNet, a late interaction model for subgraph matching, which first computes the node and edge embeddings of each graph independently of paired graph and then computes a trainable alignment map. Here, we present IsoNet++, an early interaction graph neural network (GNN), based on several technical innovations. First, we compute embeddings of all nodes by passing messages within and across the two input graphs, guided by an injective alignment between their nodes. Second, we update this alignment in a lazy fashion over multiple rounds. Within each round, we run a layerwise GNN from scratch, based on the current state of the alignment. After the completion of one round of GNN, we use the last-layer embeddings to update the alignments, and proceed to the next round. Third, IsoNet++ incorporates a novel notion of node-pair partner interaction. Traditional early interaction computes attention between a node and its potential partners in the other graph, the attention then controlling messages passed across graphs. In contrast, we consider node pairs (not single nodes) as potential partners. Existence of an edge between the nodes in one graph and non-existence in the other provide vital signals for refining the alignment. Our experiments on several datasets show that the alignments get progressively refined with successive rounds, resulting in significantly better retrieval performance than existing methods. We demonstrate that all three innovations contribute to the enhanced accuracy. Our code and datasets are publicly available at https://github.com/structlearning/isonetpp.

The problems of detecting and recovering planted structures/subgraphs in Erdős-Rényi random graphs, have received significant attention over the past three decades, leading to many exciting results and mathematical techniques. However, prior work has largely focused on specific ad hoc planted structures and inferential settings, while a general theory has remained elusive. In this paper, we bridge this gap by investigating the detection of an arbitrary planted subgraph Γ= Γ_n in an Erdős-Rényi random graph G(n, q_n), where the edge probability within Γ is p_n. We examine both the statistical and computational aspects of this problem and establish the following results. In the dense regime, where the edge probabilities p_n and q_n are fixed, we tightly characterize the information-theoretic and computational thresholds for detecting Γ, and provide conditions under which a computational-statistical gap arises. Most notably, these thresholds depend on Γ only through its number of edges, maximum degree, and maximum subgraph density. Our lower and upper bounds are general and apply to any value of p_n and q_n as functions of n. Accordingly, we also analyze the sparse regime where q_n = Θ(n^{-α}) and p_n-q_n =Θ(q_n), with αin[0,2], as well as the critical regime where p_n=1-o(1) and q_n = Θ(n^{-α}), both of which have been widely studied, for specific choices of Γ. For these regimes, we show that our bounds are tight for all planted subgraphs investigated in the literature thus farand many more. Finally, we identify conditions under which detection undergoes sharp phase transition, where the boundaries at which algorithms succeed or fail shift abruptly as a function of q_n.

Large language models have shown strong performance in natural language generation and downstream reasoning tasks, but they still struggle with logical consistency, factual grounding, and interpretability in complex multi-step reasoning. To address these limitations, this paper proposes SGR, a stepwise reasoning enhancement framework that integrates large language models with external knowledge graphs through query-relevant subgraph generation. Given an input question, SGR first extracts key entities, relations, and constraints to construct a structured schema, then retrieves compact subgraphs from a knowledge graph using schema-guided querying. The generated subgraphs provide explicit relational evidence that guides the language model through step-by-step reasoning. In addition, SGR combines direct Cypher-based reasoning with collaborative reasoning integration, allowing candidate answers from multiple reasoning paths to be validated and aggregated according to both model confidence and graph consistency. Experiments on benchmark datasets including CWQ, WebQSP, GrailQA, and KQA Pro demonstrate that SGR improves reasoning accuracy and Hits@1 performance over standard prompting and several knowledge-enhanced baselines. Ablation studies further show that schema guidance and Neo4j-based retrieval are both crucial to the effectiveness of the framework. These results indicate that dynamically generated external subgraphs can improve the accuracy, robustness, and interpretability of LLM-based reasoning.

This study aims to build a pre-trained Graph Neural Network (GNN) model on molecules without human annotations or prior knowledge. Although various attempts have been proposed to overcome limitations in acquiring labeled molecules, the previous pre-training methods still rely on semantic subgraphs, i.e., functional groups. Only focusing on the functional groups could overlook the graph-level distinctions. The key challenge to build a pre-trained GNN on molecules is how to (1) generate well-distinguished graph-level representations and (2) automatically discover the functional groups without prior knowledge. To solve it, we propose a novel Subgraph-conditioned Graph Information Bottleneck, named S-CGIB, for pre-training GNNs to recognize core subgraphs (graph cores) and significant subgraphs. The main idea is that the graph cores contain compressed and sufficient information that could generate well-distinguished graph-level representations and reconstruct the input graph conditioned on significant subgraphs across molecules under the S-CGIB principle. To discover significant subgraphs without prior knowledge about functional groups, we propose generating a set of functional group candidates, i.e., ego networks, and using an attention-based interaction between the graph core and the candidates. Despite being identified from self-supervised learning, our learned subgraphs match the real-world functional groups. Extensive experiments on molecule datasets across various domains demonstrate the superiority of S-CGIB.

Sparse GNN training reduces computation, but deciding which edges to keep can be costly. Reusing one sparse graph is cheap, but locks training to a fixed topology, while varying it across epochs can require repeated sampling or recomputation. We introduce EDiS (Edge-Disjoint Subgraph sparsification framework), which separates one-time structural extraction from per-epoch graph composition. EDiS decomposes the graph once into cacheable edge-disjoint subgraphs, then recombines them into graphs with edge-budget constraints across epochs and retention ratios without re-extracting structure. Our default construction uses feature-based scores and successive maximum score covering forests, while the same composition mechanism also supports alternative edge selection rules. We provide a combinatorial analysis of the per-epoch sampler, the composition step that draws a training graph from the cached decomposition. We show that, under the default covering-forest selector, the stored decomposition deterministically preserves high-score cut edges, and we derive a selector-agnostic conditional bound on high-score cut survival in composed training graphs. Across 19 homophilic, heterophilic, and large-scale node classification benchmarks against 17 baselines under the same edge budget, EDiS achieves the highest mean benchmark score (accuracy/ROC-AUC) and the lowest average rank and gap-to-best among ranked methods. Ablations show the clearest benefits of structural decomposition and epoch variation at tight edge budgets.

Maximum common edge subgraph (MCES) matching finds a partial vertex correspondence between two labeled graphs that preserves as many labeled edges as possible. Molecular similarity search requires matching many graph pairs, making the cost of repeated queries important. The strongest baseline attains accurate MCES solutions but trains a separate network for each pair. We introduce Equivariant Neural Primal-Dual Assignment (ENPDA), which learns a shared matching policy and applies it to new pairs without further training, answering queries roughly three orders of magnitude faster and recovering its training cost after a few dozen queries. The policy recomputes exact objective marginals for candidate matches and learns corrections and step sizes that update their scores. Target prices respond to competition when several source vertices favor the same target. Four update rounds and a Hungarian projection produce a partial one-to-one matching. We prove per-pair guarantees that hold for any network parameters. In exact arithmetic, reordering either graph permutes the assignment and price states, the projected matching is one-to-one, and repaired prices give a valid MCES upper bound. Subtracting the preserved-edge count bounds the optimality gap; combined with structural caps, these certificates prove global optimality for 60 of 291 native test pairs. On three molecular benchmarks with disjoint train/validation/test splits, ENPDA improves over an analytic counterpart with the same update and projection budget by 7.4-8.6 accuracy points; after one second of refinement search, 2.5-3 points of the gain remain. Transferred without fine-tuning to edge-deletion tasks from social and protein graphs, the policy gains 9.1-17.6 points over the analytic counterpart. When output matchings must keep aromatic rings intact, ENPDA recovers more reference bonds than the baselines on all three datasets.

Retrieval of information from graph-structured knowledge bases represents a promising direction for improving the factuality of LLMs. While various solutions have been proposed, a comparison of methods is difficult due to the lack of challenging QA datasets with ground-truth targets for graph retrieval. We present SynthKGQA, a framework for generating high-quality synthetic Knowledge Graph Question Answering datasets from any Knowledge Graph, providing the full set of ground-truth facts in the KG to reason over each question. We show how, in addition to enabling more informative benchmarking of KG retrievers, the data produced with SynthKGQA also allows us to train better models. We apply SynthKGQA to Wikidata to generate GTSQA, a new dataset designed to test zero-shot generalization abilities of KG retrievers with respect to unseen graph structures and relation types, and benchmark popular solutions for KG-augmented LLMs on it.

Information retrieval based knowledge base question answering (KBQA) first retrieves a subgraph to reduce search space, then reasons on the subgraph to select answer entities. Existing approaches have three issues that impede the retrieval of such subgraphs. Firstly, there is no off-the-shelf toolkit for semantic-relevant subgraph retrieval. Secondly, existing methods are knowledge-graph-dependent, resulting in outdated knowledge graphs used even in recent studies. Thirdly, previous solutions fail to incorporate the best available techniques for entity linking or path expansion. In this paper, we present SRTK, a user-friendly toolkit for semantic-relevant subgraph retrieval from large-scale knowledge graphs. SRTK is the first toolkit that streamlines the entire lifecycle of subgraph retrieval across multiple knowledge graphs. Additionally, it comes with state-of-the-art subgraph retrieval algorithms, guaranteeing an up-to-date solution set out of the box.

We prove that the celebrated Planar Product Structure Theorem by Dujmovic et al, and also related graph product structure results, can be formulated with the induced subgraph containment relation. Precisely, we prove that if a graph G is a subgraph of the strong product of a graph Q of bounded maximum degree (such as a path) and a graph M of bounded tree-width, then G is an induced subgraph of the strong product of Q and a graph M' of bounded tree-width being at most exponential in the maximum degree of Q and the tree-width of M. In particular, if G is planar, we show that G is an induced subgraph of the strong product of a path and a graph of tree-width 39. In the course of proving this result, we introduce and study H-clique-width, a new single structural measure that captures a hereditary analogue of the traditional product structure (where, informally, the strong product has one factor from the graph class H and one factor of bounded clique-width).

Multi-agent systems (MAS) increasingly solve complex tasks by orchestrating agents and tools selected from rapidly growing marketplaces. As these marketplaces expand, many candidates become functionally overlapping, making selection not just a retrieval problem: beyond filtering relevant agents, an orchestrator must choose options that are reliable, compatible with the current execution context, and able to cooperate with other selected agents. Existing recommender systems -- largely built for item-level ranking from flat user-item logs -- do not directly address the structured, sequential, and interaction-dependent nature of agent orchestration. We address this gap by formulating agent recommendation in MAS as a constrained decision problem and introducing a generic constrained recommendation framework that first uses retrieval to build a compact candidate set conditioned on the current subtask and context, and then performs utility optimization within this feasible set using a learned scorer that accounts for relevance, reliability, and interaction effects. We ground both the formulation and learning signals in historical calling trees, which capture the execution structure of MAS (parent-child calls, branching dependencies, and local cooperation patterns) beyond what flat logs provide. The framework supports two complementary settings: agent-level recommendation (select the next agent/tool) and system-level recommendation (select a small, connected agent team/subgraph for coordinated execution). To enable systematic evaluation, we construct a unified calling-tree benchmark by normalizing invocation logs from eight heterogeneous multi-agent corpora into a shared structured representation.

In this paper, we present "Graph Feature Preprocessor", a software library for detecting typical money laundering patterns in financial transaction graphs in real time. These patterns are used to produce a rich set of transaction features for downstream machine learning training and inference tasks such as detection of fraudulent financial transactions. We show that our enriched transaction features dramatically improve the prediction accuracy of gradient-boosting-based machine learning models. Our library exploits multicore parallelism, maintains a dynamic in-memory graph, and efficiently mines subgraph patterns in the incoming transaction stream, which enables it to be operated in a streaming manner. Our solution, which combines our Graph Feature Preprocessor and gradient-boosting-based machine learning models, can detect illicit transactions with higher minority-class F1 scores than standard graph neural networks in anti-money laundering and phishing datasets. In addition, the end-to-end throughput rate of our solution executed on a multicore CPU outperforms the graph neural network baselines executed on a powerful V100 GPU. Overall, the combination of high accuracy, a high throughput rate, and low latency of our solution demonstrates the practical value of our library in real-world applications.

In precision medicine, quantitative multi-omic features, topological context, and textual biological knowledge play vital roles in identifying disease-critical signaling pathways and targets. Existing pipelines capture only part of these-numerical omics ignore topological context, text-centric LLMs lack quantitative grounded reasoning, and graph-only models underuse node semantics and the generalization of LLMs-limiting mechanistic interpretability. Although Process Reward Models (PRMs) aim to guide reasoning in LLMs, they remain limited by unreliable intermediate evaluation, and vulnerability to reward hacking with computational cost. These gaps motivate integrating quantitative multi-omic signals, topological structure with node annotations, and literature-scale text via LLMs, using subgraph reasoning as the principle bridge linking numeric evidence, topological knowledge and language context. Therefore, we propose GALAX (Graph Augmented LAnguage model with eXplainability), an innovative framework that integrates pretrained Graph Neural Networks (GNNs) into Large Language Models (LLMs) via reinforcement guided by a Graph Process Reward Model (GPRM), which generates disease-relevant subgraphs in a step-wise manner initiated by an LLM and iteratively evaluated by a pretrained GNN, enabling process-level supervision without explicit intermediate reasoning annotations. As an application, we also introduced Target-QA, a benchmark combining CRISPR-identified targets, multi-omic profiles, and biomedical graph knowledge across diverse cancer cell lines, which enables GNN pretraining for supervising step-wise graph construction and supports long-context reasoning over text-numeric graphs (TNGs), providing a scalable and biologically grounded framework for explainable, reinforcement-guided subgraph reasoning toward reliable and interpretable target and pathway discovery in precision medicine.

Recently, large language models (LLMs) have been explored widely for 3D scene understanding. Among them, training-free approaches are gaining attention for their flexibility and generalization over training-based methods. However, they typically struggle with accuracy and efficiency in practical deployment. To address the problems, we propose Sparse3DPR, a novel training-free framework for open-ended scene understanding, which leverages the reasoning capabilities of pre-trained LLMs and requires only sparse-view RGB inputs. Specifically, we introduce a hierarchical plane-enhanced scene graph that supports open vocabulary and adopts dominant planar structures as spatial anchors, which enables clearer reasoning chains and more reliable high-level inferences. Furthermore, we design a task-adaptive subgraph extraction method to filter query-irrelevant information dynamically, reducing contextual noise and improving 3D scene reasoning efficiency and accuracy. Experimental results demonstrate the superiority of Sparse3DPR, which achieves a 28.7% EM@1 improvement and a 78.2% speedup compared with ConceptGraphs on the Space3D-Bench. Moreover, Sparse3DPR obtains comparable performance to training-based methods on ScanQA, with additional real-world experiments confirming its robustness and generalization capability.