网络模型的谱拟合优度
Spectral goodness of fit for network models
摘要：
我们引入了一个新的统计量，“光谱拟合优度”（SGOF）来衡量一个网络模型解释观察到的网络结构的程度。SGOF提供拟合的绝对度量，类似于线性回归中的标准R平方。此外，由于它利用了图拉普拉斯算子的频谱特性，因此它适用于比较各种函数形式的网络模型，包括拟合的统计模型和网络的算法生成模型。在介绍，定义和解释SGOF提供指导后，我们用一些例子和与现有技术的比较来说明统计的属性。我们表明，这样的光谱方法来评估模型拟合填补了早期方法留下的空白，可以广泛应用。
英文摘要：
We introduce a new statistic, 'spectral goodness of fit' (SGOF) to measure how well a network model explains the structure of an observed network. SGOF provides an absolute measure of fit, analogous to the standard R-squared in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.
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