We propose a statistical method for estimating the non-parametric transitivity and preferential attachment functions simultaneously in a growing network, in contrast to conventional methods that either estimate each function in isolation or assume a certain functional form for these. Our model is demonstrated to exhibit a good fit to two real-world co-authorship networks and can illuminate several intriguing details of the preferential attachment and transitivity phenomena that would be unavailable under traditional methods. Moreover, we introduce a method for quantifying the amount of contributions of these phenomena in the growth process of a network based on the probabilistic dynamic process induced by the model formula. By applying this method, we found that transitivity dominated preferential attachment in both co-authorship networks. This suggests the importance of indirect relations in scientific creative processes. The proposed method is implemented in the R package FoFaF.

我们提出了一种统计方法，用于同时估算增长网络中的非参数传递性和优先依附函数，这与常规方法不同，传统方法要么单独估计每个函数，要么为此假定某种函数形式。我们的模型被证明对两个现实世界的共同作者网络具有很好的适应性，并且可以阐明传统方法无法获得的优先附着和传递现象的几个有趣细节。此外，我们引入了一种基于模型公式诱发的概率动态过程来量化这些现象在网络的增长过程中的贡献量的方法。通过应用此方法，我们发现在两个共同作者网络中，传递性主导了优先附件。这表明间接关系在科学创造过程中的重要性。建议的方法在R包中实现FoFaF。