There is empirical evidence that collaboration in academia has increased significantly during the past few decades, perhaps due to the breathtaking advancements in communication and technology during this period. Multi-author articles have become more frequent than single-author ones. Interdisciplinary collaboration is also on the rise. Although there have been several studies on the dynamical aspects of collaboration networks, systematic statistical models which theoretically explain various empirically observed features of such networks have been lacking. In this work, we propose a dynamic mean-field model and an associated estimation framework for academic collaboration networks. We primarily focus on how the degree of collaboration of a typical author, rather than the local structure of her collaboration network, changes over time. We consider several popular indices of collaboration from the literature and study their dynamics under the proposed model. In particular, we obtain exact formulae for the expectations and temporal rates of change of these indices. Through extensive simulation experiments, we demonstrate that the proposed model has enough flexibility to capture various phenomena characteristic of real-world collaboration networks. Using metadata on papers from the arXiv repository, we empirically study the mean-field collaboration dynamics in disciplines such as Computer Science, Mathematics and Physics.

翻译：有实证证据表明，过去几十年来学术合作显著增加，可能归因于这一时期通信与技术的飞速进步。多作者论文已比单作者论文更为常见，跨学科合作也日益增多。尽管已有若干关于合作网络动态特征的研究，但尚缺乏能够从理论上解释此类网络多种实证观测特征的系统性统计模型。本文针对学术合作网络提出了一种动态平均场模型及其相应的估计框架。我们主要关注典型研究者合作程度（而非其合作网络的局部结构）随时间的变化。我们考量了文献中几种常用的合作指数，并研究了这些指数在该模型下的动态特性。具体而言，我们获得了这些指数的期望值及时间变化率的精确表达式。通过大量仿真实验，我们证明所提出的模型具有足够的灵活性来捕捉现实世界合作网络的各类典型现象。利用arXiv存储库中论文的元数据，我们实证研究了计算机科学、数学和物理学等学科中的平均场合作动态。