Graph Edit Distance Learning via Modeling Optimum Matchings with Constraints

Graph edit distance (GED) is a measure for quantifying the similarity between two graphs. Because of its flexibility and versatility, GED is widely used in many real applications. However, the main disadvantage of GED is its high computational cost. Many solutions have been proposed to speed up GED computation, but most of them focus on developing serial algorithms and only very few solutions consider parallel computing. In this paper, we study a parallel GED computation to elaborate a fast and precise algorithm. Unlike existing solutions that utilize either a depth-first or a best-first search, we propose a hybrid approach that combines depth-first and best-first search paradigms. Our approach can quickly find tighter GED upper bounds, and effectively prune the search space using the upper bounds. Based on the approach, we develop an efficient parallel GED computation algorithm named ${\sf HGED}$ . To maximize thread utility, ${\sf HGED}$ is also equipped with a novel dynamic load balancing scheme whose main focus is on reducing the overhead of thread synchronization. Experimental results on widely used real datasets show that, on average, ${\sf HGED}$ outperforms the state-of-the art serial algorithm ${\sf AStar}^{+}$ - ${\sf LSa}$ by 6 times and the state-of-the parallel algorithm ${\sf PGED}$ by 4 times.

Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently, the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation, we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

Graph edit distance is an error tolerant matching technique emerged as a powerful and flexible graph matching paradigm that can be used to address different tasks in pattern recognition, machine learning and data mining; it represents the minimum-cost sequence of basic edit operations to transform one graph into another by means of insertion, deletion and substitution of vertices and/or edges. A widely used method for exact graph edit distance computation is based on the A* algorithm. To overcome its high memory load while traversing the search tree for storing pending solutions to be explored, we propose a depth-first graph edit distance algorithm which requires less memory and searching time. An evaluation of all possible solutions is performed without explicitly enumerating them all. Candidates are discarded using an upper and lower bounds strategy. A solid experimental study is proposed; experiments on a publicly available database empirically demonstrated that our approach is better than the A* graph edit distance computation in terms of speed, accuracy and classification rate.

The definition of efficient similarity or dissimilarity measures between graphs is a key problem in structural pattern recognition. This problem is nicely addressed by the graph edit distance, which constitutes one of the most flexible graph dissimilarity measure in this field. Unfortunately, the computation of an exact graph edit distance is known to be exponential in the number of nodes. In the early beginning of this decade, an efficient heuristic based on a bipartite assignment algorithm has been proposed to find efficiently a suboptimal solution. This heuristic based on an optimal matching of nodes' neighborhood provides a good approximation of the exact edit distance for graphs with a large number of different labels and a high density. Unfortunately, this heuristic works poorly on unlabeled graphs or graphs with a poor diversity of neighborhoods. In this work we propose to extend this heuristic by considering a mapping of bags of walks centered on each node of both graphs.

A novel hierarchical-based framework for upper bound computation of graph edit distance

Graph neural networks (GNNs) are increasingly used to model complex patterns in graph-structured data. However, enabling them to ''forget'' designated information remains challenging, especially under privacy regulations such as the GDPR. Existing unlearning methods largely optimize for efficiency and scalability, yet they offer little transparency, and the black-box nature of GNNs makes it difficult to verify whether forgetting has truly occurred. We propose an explainability-driven verifier for GNN unlearning that snapshots the model before and verifies after deletion, using attribution shifts and localized structural changes (e.g., graph edit distance) as transparent evidence. The verifier uses five explainability metrics—residual attribution, heatmap shift, explainability score deviation, graph edit distance, and (diagnostic) graph rule shift. We evaluate two backbones (GCN, GAT) and four unlearning strategies (Retrain, GraphEditor, GNNDelete, IDEA) across five benchmarks (Cora, Citeseer, Pubmed, Coauthor?CS, Coauthor?Physics). Results show that Retrain and GNNDelete achieve near-complete forgetting, GraphEditor provides partial erasure, and IDEA leaves residual signals. These explanation deltas provide the primary, human-readable evidence of forgetting; we also report membership?inference ROC?AUC as a complementary, graph?wide privacy signal. The code is available at https://github.com/ImranAhsan23/F-E

Learning graph edit distance by graph neural networks

It is essential to identify similarity between graphs for various tasks in data mining, machine learning and pattern recognition. Graph edit distance (GED) is the most popular graph similarity measure thanks to its flexibility and versatility. In this paper, we study the problem of top-<i>k</i> graph similarity search, which finds <i>k</i> graphs most similar to a given query graph under the GED measure. We propose incremental GED computation algorithms that compute desired GED lower and upper bounds. Based on the algorithms, we develop novel search frameworks to address the top-<i>k</i> search problem. Our frameworks are also designed to use a state-of-the art indexing technique to speed up top-<i>k</i> search. By conducting extensive experiments on real datasets, we show that the proposed frameworks significantly improve the performance of top-<i>k</i> graph similarity search.

Image categorization: Graph edit [formula omitted] direction histogram

In the "blind review" mode for technical bid evaluation within the power industry, review experts must make impartial judgments based on anonymized technical response documents. However, these documents often contain a large amount of complex graphical content, which existing general Optical Character Recognition (OCR) technology struggles to accurately identify. To address this, this study first constructs a specialized image dataset covering typical power industry response document scenarios. Subsequently, an improved You Only Look Once (YOLO) object detection model is developed, incorporating an anchor box clustering strategy optimized for small, densely packed power symbols and a multi-scale feature fusion mechanism. Then, a local contextual relationship inference module based on Graph Neural Networks is designed and integrated. Finally, an end-to-end recognition pipeline from image input to structured information output is constructed. Experimental results indicate that the improved model achieves a mean Average Precision (mAP) of 90.0% in key equipment detection tasks; in topology relationship restoration experiments, the average Graph Edit Distance (GED) is 0.172; in end-to-end efficiency experiments simulating real blind review scenarios, the average processing time per document is only 8.7 seconds, with an information completeness rate of 98.2%. The research demonstrates that the YOLO-based object detection and relationship modeling method, customized for the blind review mode, can effectively address the challenge of recognizing complex image content in power response documents, providing reliable technical support for the efficiency and fairness of blind reviews.

Background Graph edit distance is a methodology used to solve error-tolerant graph matching. This methodology estimates a distance between two graphs by determining the minimum number of modifications required to transform one graph into the other. These modifications, known as edit operations, have an edit cost associated that has to be determined depending on the problem.Objective This study focuses on the use of optimization techniques in order to learn the edit costs used when comparing graphs by means of the graph edit distance.Methods Graphs represent reduced structural representations of molecules using pharmacophore-type node descriptions to encode the relevant molecular properties. This reduction technique is known as extended reduced graphs. The screening and statistical tools available on the ligand-based virtual screening benchmarking platform and the RDKit were used.ResultsIn the experiments, the graph edit distance using learned costs performed better or equally good than using predefined costs. This is exemplified with six publicly available datasets: DUD-E, MUV, GLL&GDD, CAPST, NRLiSt BDB, and ULS-UDS.Conclusion This study shows that the graph edit distance along with learned edit costs is useful to identify bioactivity similarities in a structurally diverse group of molecules. Furthermore, the target-specific edit costs might provide useful structure-activity information for future drug-design efforts.

Explaining the foundations for predictions obtained from graph neural networks (GNNs) is critical for credible use of GNN models for real-world problems. Owing to the rapid growth of GNN applications, recent progress in explaining predictions from GNNs, such as sensitivity analysis, perturbation methods, and attribution methods, showed great opportunities and possibilities for explaining GNN predictions. In this study, we propose a method to improve the explanation quality of node classification tasks that can be applied in a post hoc manner through aggregation of auxiliary explanations from important neighboring nodes, named SEEN. Applying SEEN does not require modification of a graph and can be used with diverse explainability techniques due to its independent mechanism. Experiments on matching motifparticipating nodes from a given graph show great improvement in explanation accuracy of up to 12.71% and demonstrate the correlation between the auxiliary explanations and the enhanced explanation accuracy through leveraging their contributions. SEEN provides a simple but effective method to enhance the explanation quality of GNN model outputs, and this method is applicable in combination with most explainability techniques.

Comparison of RNA structures is one of the most crucial analysis for elucidating their individual functions and promoting medical applications. Because it is widely accepted that their functions and structures are strongly correlated, various methods for RNA secondary structure analysis have been proposed owing to the difficulty in predicting RNA three-dimensional structure directly from its sequence. However, there are few methods dealing with RNA secondary structures with a specific and complex partial structure called pseudoknot despite its significance to biological process, which is a big obstacle for analyzing their functions. In this study, we propose a novel tree representation of pseudoknotted RNA secondary structures by topological centroid identification and their comparison methods based on the tree edit distance. In the proposed method, a given graph representing an RNA secondary structure is transformed to a tree rooted at one of the vertices constituting the topological centroid that is identified by removing cycles with peeling processing for the graph. When comparing tree-represented RNA secondary structures collected from a public database using the tree edit distance and functional gene groups defined by Gene Ontology (GO), the proposed method showed better clustering results according to their GOs than canonical RNA sequence-based comparison. In addition, we also report a case that the combination of the tree edit distance and the sequence edit distance shows a better classification of the pseudoknotted RNA secondary structures.

Network alignment is an important technique with applications in diverse domains, such as social network analysis, bioinformatics, and knowledge graph construction. Many of the alignment methods rely on predefined anchor nodes, which are often unavailable in real-world scenarios. To overcome this limitation, we propose MANNA (MAtched Neighbor consistency for Network Alignment), an unsupervised approach to network alignment that exploits the concept of Matched Neighborhood Consistency (MNC). The hypothesis of MANNA is that nodes with higher similarity within their local neighborhood structures are more likely to be aligned across different networks. To learn the structural and attribute features of networks, MANNA uses a Graph Neural Network (GNN). It extracts multi-order node embeddings to capture multi-scale neighborhood features, which are then used to construct similarity matrices for the alignment process. MANNA introduces a key innovation by using pseudo-anchor nodes identified by the MNC strategy to provide self-supervised learning signals in the absence of real anchor nodes. This approach enhances the model’s ability to learn accurate network representations and improve alignment accuracy. Alignment results are iteratively refined by applying the MNC strategy, which strengthens the consistency of neighborhood structures between matched nodes. Extensive experiments on three public datasets show that MANNA outperforms existing network alignment methods.

The secure computation of the graph structure is an important element in the field of secure calculation of graphs, which is important in querying data in graphs, since there are no algorithms for the graph edit distance problem that can resist attacks by malicious adversaries. In this paper, for the problem of secure computation of similarity edit distance of graphs, firstly, the encoding method applicable to the Paillier encryption algorithm is proposed, and the XOR operation scheme is proposed according to the Paillier homomorphic encryption algorithm. Then, the security algorithm under the semi-honest model is designed, which adopts the new encoding method and the XOR operation scheme. Finally, for the malicious behaviors that may be implemented by malicious participants in the semi-honest algorithm, using the hash function, a algorithm for secure computation of graph editing distance under the malicious model is designed, and the security of the algorithm is proved, and the computational complexity and the communication complexity of the algorithm are analyzed, which is more efficient compared with the existing schemes, and has practical value. The algorithm designed in this paper fills the research gap in the existing literature on the problem of graph edit distance and contributes to solving the problem.