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Graph neural networks (GNNs) extend convolutional neural networks (CNNs) tograph-based data. A question that arises is how much performance improvementdoes the underlying graph structure in the GNN provide over the CNN (thatignores this graph structure). To address this question, we introduce edgeentropy and evaluate how good an indicator it is for possible performanceimprovement of GNNs over CNNs. Our results on node classification withsynthetic and real datasets show that lower values of edge entropy predictlarger expected performance gains of GNNs over CNNs, and, conversely, higheredge entropy leads to expected smaller improvement gains.

Edge Entropy as an Indicator of the Effectiveness of GNNs over CNNs for Node Classification