Peixoto Tiago P
Department of Network and Data Science, Central European University, 1100 Vienna, Austria.
Phys Rev E. 2022 Aug;106(2-1):024305. doi: 10.1103/PhysRevE.106.024305.
We develop a method to infer community structure in directed networks where the groups are ordered in a latent one-dimensional hierarchy that determines the preferred edge direction. Our nonparametric Bayesian approach is based on a modification of the stochastic block model (SBM), which can take advantage of rank alignment and coherence to produce parsimonious descriptions of networks that combine ordered hierarchies with arbitrary mixing patterns between groups. Since our model also includes directed degree correction, we can use it to distinguish nonlocal hierarchical structure from local in- and out-degree imbalance-thus, removing a source of conflation present in most ranking methods. We also demonstrate how we can reliably compare with the results obtained with the unordered SBM variant to determine whether a hierarchical ordering is statistically warranted in the first place. We illustrate the application of our method on a wide variety of empirical networks across several domains.
我们开发了一种方法来推断有向网络中的社区结构，其中组在潜在的一维层次结构中排序，该层次结构决定了首选的边方向。我们的非参数贝叶斯方法基于对随机块模型（SBM）的修改，它可以利用秩对齐和连贯性来生成对网络的简洁描述，这些描述将有序层次结构与组之间的任意混合模式结合起来。由于我们的模型还包括有向度校正，我们可以用它来区分非局部层次结构与局部入度和出度不平衡，从而消除大多数排名方法中存在的混淆源。我们还展示了如何可靠地与无序SBM变体获得的结果进行比较，以首先确定层次排序在统计上是否合理。我们说明了我们的方法在多个领域的各种实证网络上的应用。
