Community structure is common in many real networks, with nodes clustered in groups sharing the same connections patterns. While many community detection methods have been developed for networks with binary edges, few of them are applicable to networks with weighted edges, which are common in practice. We propose a pseudo-likelihood community estimation algorithm derived under the weighted stochastic block model for networks with normally distributed edge weights, extending the pseudo-likelihood algorithm for binary networks, which offers some of the best combinations of accuracy and computational efficiency. We prove that the estimates obtained by the proposed method are consistent under the assumption of homogeneous networks, a weighted analogue of the planted partition model, and show that they work well in practice for both homogeneous and heterogeneous networks. We illustrate the method on simulated networks and on a fMRI dataset, where edge weights represent connectivity between brain regions and are expected to be close to normal in distribution by construction.

翻译：社区结构在众多真实网络中普遍存在，节点聚集形成具有相同连接模式的组团。尽管已有许多针对二值边网络的社区检测方法，但鲜有方法适用于实践中常见的加权边网络。我们提出一种基于加权随机块模型的伪似然社区估计算法，该模型假定边权服从正态分布，从而将二值网络中的伪似然算法（该算法在准确性与计算效率的综合表现上最为出色）扩展至加权场景。我们证明，在齐次网络（即加权版植入分区模型）假设下，该方法获得的估计量具有一致性，并在齐次与异质网络中均展现出良好实践效果。通过模拟网络及功能磁共振成像数据集（其中边权表示脑区间的连接强度，且其分布构建时接近正态）验证了该方法。