In community detection, many methods require the user to specify the number of clusters in advance since an exhaustive search over all possible values is computationally infeasible. While some classical algorithms can infer this number directly from the data, this is typically not the case for graph neural networks (GNNs): even when a desired number of clusters is specified, standard GNN-based methods often fail to return the exact number due to the way they are designed. In this work, we address this limitation by introducing a flexible and principled way to control the number of communities discovered by GNNs. Rather than assuming the true number of clusters is known, we propose a framework that allows the user to specify a plausible range and enforce these bounds during training. However, if the user wants an exact number of clusters, it may also be specified and reliably returned.

翻译：在社区检测中，许多方法要求用户预先指定聚类数量，因为对所有可能值进行穷举搜索在计算上不可行。虽然某些经典算法可以直接从数据中推断出这一数量，但图神经网络通常无法做到这一点：即使指定了期望的聚类数量，基于GNN的标准方法也常因其设计方式而无法返回确切数量。在本工作中，我们通过引入一种灵活且规范的方法来解决这一局限，从而控制GNN发现的社区数量。我们不再假设真实聚类数量已知，而是提出一个允许用户指定合理范围并在训练过程中强制执行这些界限的框架。然而，若用户需要确切的聚类数量，也可指定并可靠地返回该数值。