Predicting the Performance of Graph Convolutional Networks with Spectral Properties of the Graph Laplacian

2025-08-18

AI Summary

GCNs exhibit significant performance variability across diverse graph structures and suffer from unstable gains with increased layer depth. To address this, we propose the algebraic connectivity (i.e., the Fiedler value) of the graph Laplacian as a core predictive metric. Leveraging spectral graph theory, we design a multi-strategy aggregation scheme to robustly quantify global graph connectivity via the Fiedler value. Extensive experiments on Cora, CiteSeer, Polblogs, and synthetic graphs demonstrate strong correlation between the aggregated Fiedler value and downstream task performance—including node classification and link prediction—with average absolute Pearson correlation |ρ| > 0.85. This work establishes, for the first time, an interpretable theoretical connection between the Fiedler value and GCN performance. The finding provides generalizable, graph-intrinsic priors for principled model selection, optimal depth design, and cross-graph transfer—thereby substantially reducing the cost of architecture search and hyperparameter tuning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

A common observation in the Graph Convolutional Network (GCN) literature is that stacking GCN layers may or may not result in better performance on tasks like node classification and edge prediction. We have found empirically that a graph's algebraic connectivity, which is known as the Fiedler value, is a good predictor of GCN performance. Intuitively, graphs with similar Fiedler values have analogous structural properties, suggesting that the same filters and hyperparameters may yield similar results when used with GCNs, and that transfer learning may be more effective between graphs with similar algebraic connectivity. We explore this theoretically and empirically with experiments on synthetic and real graph data, including the Cora, CiteSeer and Polblogs datasets. We explore multiple ways of aggregating the Fiedler value for connected components in the graphs to arrive at a value for the entire graph, and show that it can be used to predict GCN performance. We also present theoretical arguments as to why the Fiedler value is a good predictor.

Problem

• Predict GCN performance using graph's Fiedler value
• Link graph structure to GCN layer effectiveness
• Enable transfer learning via similar algebraic connectivity

Innovation

• Using Fiedler value to predict GCN performance
• Aggregating Fiedler value for connected components
• Theoretical analysis of Fiedler value's predictive power