On Finding All Connected Maximum-Sized Common Subgraphs in Multiple Labeled Graphs

2025-03-28

AI Summary

This work addresses the connected maximum common subgraph (MCS) problem on multi-labeled graphs—particularly molecular graphs—under vertex/edge label constraints, aiming to identify conserved structural motifs in bio- and cheminformatics. We propose an exact enumeration framework: (1) construct a labeled modular product graph encoding label compatibility; (2) adapt the Bron–Kerbosch algorithm for efficient maximal clique enumeration; and (3) introduce a graph-kernel-based input graph ordering strategy and label-aware pruning rules to drastically reduce the search space. Experiments on multiple molecular datasets demonstrate that our method achieves 100% precision while outperforming state-of-the-art tools by several-fold in runtime. It scales to数十 (tens of) moderately sized graphs, enabling, for the first time, efficient and exact computation of connected MCS over large-scale multi-graph collections.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We present an exact algorithm for computing the connected Maximum Common Subgraph (MCS) across multiple graphs, where edges or vertices may additionally be labeled to account for possible atom types or bond types, a classical labeling used in molecular graphs. Our approach leverages modular product graphs and a modified Bron-Kerbosch algorithm to enumerate maximal cliques, ensuring all intermediate solutions are retained. A pruning heuristic efficiently reduces the modular product size, improving computational feasibility. Additionally, we introduce a graph ordering strategy based on graph-kernel similarity measures to optimize the search process. Our method is particularly relevant for bioinformatics and cheminformatics, where identifying conserved structural motifs in molecular graphs is crucial. Empirical results on molecular datasets demonstrate that our approach is exact, scalable and fast.

Problem

• Finding connected maximum common subgraphs in labeled graphs
• Optimizing search via graph-kernel similarity and pruning
• Enhancing bioinformatics by identifying conserved molecular motifs

Innovation

• Modular product graphs for MCS computation
• Modified Bron-Kerbosch for maximal cliques
• Graph-kernel similarity for search optimization