论文标题
加权签名网络中模块化的渐近分布
The Asymptotic Distribution of Modularity in Weighted Signed Networks
论文作者
论文摘要
模块化是一个流行的指标，用于量化网络内社区结构的程度。对网络边缘重量或邻接矩阵的最大特征值的分布进行了充分的研究，并且在执行统计推断时经常用作模块化的替代品。但是，我们表明，最大的特征值和模块化是渐近不相关的，这表明当网络大小较大时，需要直接推断模块化本身。为此，在网络的边缘权重矩阵属于高斯正交集合并研究在某些替代模型下对社区结构的相应测试的统计能力的情况下，我们得出了模块化的渐近分布。我们从经验上探索了限制分布的通用性扩展，并通过I型错误模拟证明了这些渐近分布的准确性。我们还将基于模块化测试的经验能力与一些现有方法进行了比较。然后，我们的方法用于测试两个实际数据应用程序中社区结构的存在。
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a substitute for modularity when performing statistical inference. However, we show that the largest eigenvalue and modularity are asymptotically uncorrelated, which suggests the need for inference directly on modularity itself when the network size is large. To this end, we derive the asymptotic distributions of modularity in the case where the network's edge weight matrix belongs to the Gaussian Orthogonal Ensemble, and study the statistical power of the corresponding test for community structure under some alternative model. We empirically explore universality extensions of the limiting distribution and demonstrate the accuracy of these asymptotic distributions through type I error simulations. We also compare the empirical powers of the modularity based tests with some existing methods. Our method is then used to test for the presence of community structure in two real data applications.
