Performance Analysis of Graph Laplacian Matrices in Node Classification

Graph neural networks have received great attention in recent years due to their wide range of applications. In particular, the use of graph convolutional networks to deal with classification tasks has seen rapid advancements recently. This paper explores a critical step in processing input data for graph convolutional networks, the so-called “normalization of the graph Laplacian matrix”. Two commonly used graph Laplacian matrices normalization schemes, symmetric normalized Laplacian matrix and random walk normalized Laplacian matrix, are analyzed and compared in this research. Critical discoveries are explained through experiments and benchmarking evaluation. The result shows that the symmetric normalized Laplacian matrix is suitable for denser graphs, while the random walk normalized Laplacian matrix is more feasible for sparser graph-based operations.