Community detection for unweighted networks has been widely studied in network analysis, but the case of weighted networks remains a challenge. This paper proposes a general Distribution-Free Model (DFM) for weighted networks in which nodes are partitioned into different communities. DFM can be seen as a generalization of the famous stochastic blockmodels from unweighted networks to weighted networks. DFM does not require prior knowledge of a specific distribution for elements of the adjacency matrix but only the expected value. In particular, signed networks with latent community structures can be modeled by DFM. We build a theoretical guarantee to show that a simple spectral clustering algorithm stably yields consistent community detection under DFM. We also propose a four-step data generation process to generate adjacency matrices with missing edges by combining DFM, noise matrix, and a model for unweighted networks. Using experiments with simulated and real datasets, we show that some benchmark algorithms can successfully recover community membership for weighted networks generated by the proposed data generation process.

翻译：无权网络的社区检测在网络分析中已被广泛研究，但加权网络的情况仍然是一个挑战。本文提出了一种通用的无分布模型（DFM），用于将节点划分为不同社区的加权网络。DFM可视为著名的随机块模型从无权网络到加权网络的推广。DFM无需预先知道邻接矩阵元素的具体分布，仅需其期望值。特别地，具有潜在社区结构的符号网络可通过DFM进行建模。我们提供了理论保证，证明简单的谱聚类算法在DFM下能够稳定实现一致的社区检测。我们还提出了一种四步数据生成过程，通过结合DFM、噪声矩阵和无权网络模型来生成带有缺失边的邻接矩阵。通过模拟和真实数据集的实验，我们证明了一些基准算法能够成功恢复由所提数据生成过程产生的加权网络的社区成员。