discrete subgraph extraction

Graph neural networks (GNNs) often suffer from semantic information loss during pooling operations in graph classification, which hinders their ability to provide interpretability at both subgraph and graph levels. To address this limitation, this work proposes the Subgraph Concept Network (SCN), which employs soft clustering of node concept embeddings to jointly and end-to-end distill semantic concepts at both subgraph and graph granularities. SCN is the first method to enable collaborative learning of multi-level concepts within GNNs, thereby overcoming the conventional reliance on node embeddings alone for interpretation. The approach achieves competitive graph classification performance while significantly enhancing model interpretability through explicit, hierarchical concept discovery.

Addressing the challenge of jointly achieving discriminative power and interpretability in graph-level prediction tasks, this paper proposes the Explainable Interaction Network (EIN) framework. EIN is the first approach to seamlessly integrate exact subgraph isomorphism enumeration with graph neural networks (GNNs) in an end-to-end manner, enabling explicit modeling of task-critical substructures. It further introduces a sparse regularization scheme that automatically prunes non-informative subgraphs and identifies salient ones, thereby enhancing intrinsic interpretability without compromising computational efficiency. Crucially, EIN requires neither handcrafted subgraph templates nor post-hoc explanation methods, offering both structural awareness and built-in interpretability. Extensive experiments on multiple benchmark datasets demonstrate that EIN matches or surpasses state-of-the-art GNNs in predictive accuracy while precisely localizing semantically meaningful subgraph patterns decisive for model decisions—establishing a novel paradigm for interpretable graph learning.

This work studies the learning-augmented densest subgraph problem: given a partial solution from a lightweight classifier—covering at least a $(1-varepsilon)$ fraction of the nodes in the optimal subgraph—we propose the first linear-time algorithm with theoretical guarantee of outputting a $(1-varepsilon)$-approximate solution. Our method abandons traditional LP or maximum-flow solvers, instead integrating greedy refinement with density-driven pruning to tightly couple prediction signals with combinatorial optimization. The key contribution is the first rigorous integration of supervised node classification with a minimal combinatorial algorithm, achieving both strong approximation guarantees and low computational overhead. The framework naturally extends to directed graphs and NP-hard variants—including constrained and weighted densest subgraph problems. On the Twitch Ego Nets dataset, our algorithm significantly outperforms Charikar’s algorithm and pure prediction baselines, demonstrating high accuracy, efficiency, and generalization across problem variants.

Subgraph counting on graph data faces an inherent trade-off between expressive power and computational efficiency. Method: This paper proposes the Localized Weisfeiler–Leman (Local k-WL) framework, introducing a novel subgraph fragmentation decomposition technique that enables exact counting of all induced subgraphs of size ≤4 using only 1-WL. The approach integrates a three-tier differentiable learning architecture, bridging combinatorial algorithms with end-to-end GNN training, and rigorously proves its expressive power lies strictly between k-WL and (k+1)-WL. Contribution/Results: Compared to standard k-WL, Local k-WL achieves significantly lower time and space complexity. Experiments on computational biology and social network datasets demonstrate superior performance in counting accuracy, generalization, and inference efficiency—establishing a new state-of-the-art for scalable, expressive subgraph counting.

The densest subgraph problem (DSP) and related monotonic ratio optimization problems—including conductance, the Cheeger constant, and normalized cut—suffer from high computational complexity in exact algorithms and suboptimal solutions in heuristic approaches. Method: We propose Incremental Parametric Cut (IPC), a novel framework that integrates network flow techniques with parametric programming to achieve fast, globally optimal solutions. Contribution/Results: IPC is the first systematically implemented and empirically validated method demonstrating efficiency on large-scale graphs: its time complexity is significantly lower than that of full parametric min-cut, it outperforms state-of-the-art heuristics in speed, and it guarantees global optimality. Experiments confirm IPC’s strong scalability and generalization across diverse graph partitioning tasks. We release open-source code and a standardized benchmark suite, establishing a new paradigm for monotonic ratio optimization.

This work addresses the scalability bottleneck in subgraph pattern detection within large-scale graphs, a challenge rooted in the NP-completeness of the problem, by introducing the DETR paradigm to this task for the first time. The proposed method formulates subgraph detection as a set prediction problem, leveraging a graph neural network to encode the target graph, learnable query embeddings, and a Transformer decoder to jointly predict all pattern instances in an end-to-end manner via bipartite matching loss. This framework supports both exact and approximate pattern matching, thereby overcoming the limitation of traditional approaches that are restricted to exact structural matches. Experiments demonstrate that the method efficiently detects diverse patterns of up to 50 nodes in graphs containing 1,000 nodes, achieving an AP₁₀₀ of 91.2 on functional group detection in the ChEMBL molecular dataset.

Subgraph extraction problems arise widely in network design, facility location, and related domains, yet lack a general-purpose, efficient solution methodology. This work proposes ΔSearch—the first unified heuristic framework that requires only user-specified feasibility constraints and an optimization objective, automatically adapting to monotone, weighted monotone, and non-monotone graph problems without problem-specific parameter tuning. By integrating a reward-penalty optimization mechanism, generic constraint modeling, and search space pruning techniques, ΔSearch substantially enhances computational efficiency and can accelerate exact algorithms. Empirical evaluations demonstrate that it matches or surpasses state-of-the-art heuristics on tasks such as maximum planar subgraph, uncapacitated facility location, and prize-collecting vertex cover, while achieving approximately 89% of optimal solution quality on average across other problems—all without any parameter tuning.

Existing visual graph recognition methods are often confined to specific tasks and lack generalizability and cross-scenario transferability. This work proposes GraSP, an end-to-end framework based on subgraph prediction that jointly models graph structure and visual features to enable unified recognition of diverse graph types and rendering styles. GraSP achieves cross-task transfer without task-specific fine-tuning, representing the first general-purpose and transferable approach for visual graph recognition. Evaluated on multiple synthetic benchmarks and a real-world application, GraSP demonstrates exceptional generalization and adaptability, advancing the field toward a unified paradigm for graph recognition.

This work addresses the challenge of unifying the representation of conditional independence structures induced by feedback, latent variables, and selection mechanisms. It proposes a class of separable graphical models based on mixed graphs containing directed, undirected, and bidirected edges, where the absence of an edge corresponds to a separating set between its endpoints. By introducing separable graphs and their essential forms, the framework subsumes several existing graphical models. The study establishes an equivalence among graph structure, separation properties, and canonical parametrization, and leverages this correspondence to design an algorithm for identifying equivalence classes. Under mild assumptions, the algorithm consistently recovers the separation-equivalence class of a separable graph, thereby providing both theoretical foundations and computational tools for modeling and learning complex dependency structures.