Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models are capable of addressing two prominent topics in network science: link prediction and community detection. However, such methods often have a resolution limit, making it difficult to separate small-scale structures from noise. To arrive at a smoother representation of the network's generative mechanism, we explicitly trade variance for bias by smoothing blocks of edges based on stochastic equivalence. As such, we propose a different estimation method using a new model, which we call the stochastic shape model. Typically, analysis methods are based on modelling node or link communities. In contrast, we take a hybrid approach, bridging the two notions of community. Consequently, we obtain a more parsimonious representation, enabling a more interpretable and multiscale summary of the network structure. By considering multiple resolutions, we trade bias and variance to ensure that our estimator is rate-optimal. We also examine the performance of our model through simulations and applications to real network data.

翻译：网络作为研究复杂系统中大规模连接模式的工具，其生成机制的非参数建模通常基于阶梯函数（如随机块模型）。这类模型能够解决网络科学中的两大核心问题：链接预测与社区检测。然而，此类方法常存在分辨率限制，难以将小尺度结构从噪声中分离。为获得更平滑的网络生成机制表征，我们基于随机等价性对边块进行显式平滑处理，通过权衡方差与偏置误差。基于此，我们提出采用新模型（称为随机形状模型）的不同估计方法。传统分析方法通常基于节点社区或链接社区建模，而本工作则采用混合方法，融合这两种社区概念。由此获得更简洁的表征，实现更具可解释性与多尺度的网络结构总结。通过考虑多分辨率，我们平衡偏置与方差以确保估计器的速率最优性。最后通过模拟实验与真实网络数据验证模型性能。