School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, People's Republic of China.
Sci Rep. 2022 Sep 7;12(1):15153. doi: 10.1038/s41598-022-19456-2.
A degree-corrected distribution-free model is proposed for weighted social networks with latent structural information. The model extends the previous distribution-free models by considering variation in node degree to fit real-world weighted networks, and it also extends the classical degree-corrected stochastic block model from un-weighted network to weighted network. We design an algorithm based on the idea of spectral clustering to fit the model. Theoretical framework on consistent estimation for the algorithm is developed under the model. Theoretical results when edge weights are generated from different distributions are analyzed. We also propose a general modularity as an extension of Newman's modularity from un-weighted network to weighted network. Using experiments with simulated and real-world networks, we show that our method significantly outperforms the uncorrected one, and the general modularity is effective.
提出了一种具有潜在结构信息的加权社交网络的无分布修正模型。该模型通过考虑节点度的变化来扩展以前的无分布模型，以适应现实世界中的加权网络，并且还将经典的度修正随机块模型从无加权网络扩展到加权网络。我们设计了一种基于谱聚类思想的算法来拟合模型。在模型下开发了用于算法的一致估计的理论框架。分析了从不同分布生成边缘权重时的理论结果。我们还提出了一种通用模块度，作为纽曼模块度从无加权网络到加权网络的扩展。通过使用模拟和真实网络的实验，我们表明我们的方法明显优于未修正的方法，并且通用模块度是有效的。
