Spectral methods provide consistent estimators for community detection in dense graphs. However, their performance deteriorates as the graphs become sparser. In this work we consider a random graph model that can produce graphs at different levels of sparsity, and we show that graph neural networks can outperform spectral methods on sparse graphs. We illustrate the results with numerical examples in both synthetic and real graphs.

翻译：光谱方法为密度图形中的社区探测提供了一致的测算符。 然而, 它们的性能随着图形变得稀疏而恶化。 在这项工作中, 我们考虑一个随机的图形模型, 可以在不同层次的宽度上生成图形, 我们显示, 图形神经网络可以在稀薄图形上优于光谱方法。 我们用合成图和真实图中的数字示例来说明结果 。