Graph Coordinates and Conventional Neural Networks -- An Alternative for Graph Neural Networks

Graph-based data present unique challenges and opportunities for machine learning. Graph Neural Networks (GNNs), and especially those algorithms that capture graph topology through message passing for neighborhood aggregation, have been a leading solution. However, these networks often require substantial computational resources and may not optimally leverage the information contained in the graph's topology, particularly for large-scale or complex graphs. We propose Topology Coordinate Neural Network (TCNN) and Directional Virtual Coordinate Neural Network (DVCNN) as novel and efficient alternatives to message passing GNNs, that directly leverage the graph's topology, sidestepping the computational challenges presented by competing algorithms. Our proposed methods can be viewed as a reprise of classic techniques for graph embedding for neural network feature engineering, but they are novel in that our embedding techniques leverage ideas in Graph Coordinates (GC) that are lacking in current practice. Experimental results, benchmarked against the Open Graph Benchmark Leaderboard, demonstrate that TCNN and DVCNN achieve competitive or superior performance to message passing GNNs. For similar levels of accuracy and ROC-AUC, TCNN and DVCNN need far fewer trainable parameters than contenders of the OGBN Leaderboard. The proposed TCNN architecture requires fewer parameters than any neural network method currently listed in the OGBN Leaderboard for both OGBN-Proteins and OGBN-Products datasets. Conversely, our methods achieve higher performance for a similar number of trainable parameters. By providing an efficient and effective alternative to message passing GNNs, our work expands the toolbox of techniques for graph-based machine learning.