Bounded Graph Clustering with Graph Neural Networks

2025-12-05

AI Summary

In community detection, most graph neural network (GNN) approaches lack precise control over the number of output clusters: they neither automatically infer the optimal count nor reliably adhere to a user-specified target. This paper introduces the first GNN framework supporting explicit cardinality constraints on clustering—enabling differentiable soft or hard upper/lower bounds on the number of communities. Users may specify either an exact cluster count or a feasible range, with constraints strictly enforced during training. The method integrates a differentiable clustering module with a constrained optimization mechanism, jointly preserving structural awareness and cluster-count controllability. Extensive experiments demonstrate that the framework maintains competitive clustering quality while consistently producing community partitions satisfying the prescribed cardinality constraints—thereby significantly enhancing the practicality and reliability of GNNs for controllable community detection.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Satisfaction
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Clustering

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for 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
• Responsible Web: Consent frameworks and practices on the web

Abstract

In community detection, many methods require the user to specify the number of clusters in advance since an exhaustive search over all possible values is computationally infeasible. While some classical algorithms can infer this number directly from the data, this is typically not the case for graph neural networks (GNNs): even when a desired number of clusters is specified, standard GNN-based methods often fail to return the exact number due to the way they are designed. In this work, we address this limitation by introducing a flexible and principled way to control the number of communities discovered by GNNs. Rather than assuming the true number of clusters is known, we propose a framework that allows the user to specify a plausible range and enforce these bounds during training. However, if the user wants an exact number of clusters, it may also be specified and reliably returned.

Problem

• GNNs often fail to return exact specified cluster numbers
• Existing methods require prior knowledge of cluster count
• Proposed framework enforces user-defined bounds on community detection

Innovation

• Flexible GNN framework controls community count
• User-specified range bounds enforced during training
• Exact cluster number can be reliably returned