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

TL;DR

This paper demonstrates that the algebraic connectivity, or Fiedler value, of a graph can predict the performance of Graph Convolutional Networks, aiding in transfer learning and hyperparameter selection.

Contribution

It introduces the Fiedler value as a spectral predictor of GCN performance, supported by theoretical insights and empirical validation on various datasets.

Findings

Fiedler value correlates with GCN accuracy across datasets

Graphs with similar Fiedler values exhibit similar GCN performance

Theoretical justification for using algebraic connectivity as a predictor

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.