The preferential attachment (PA) model is a popular way of modeling dynamic social networks, such as collaboration networks. Assuming that the PA function takes a parametric form, we propose and study the maximum likelihood estimator of the parameter. Using a supercritical continuous-time branching process framework, we prove the almost sure consistency and asymptotic normality of this estimator. We also provide an estimator that only depends on the final snapshot of the network and prove its consistency, and its asymptotic normality under general conditions. We compare the performance of the estimators to a nonparametric estimator in a small simulation study.

翻译：优惠附加(PA)模式是模拟充满活力的社会网络,例如协作网络的一种流行方式。假设PA函数采取参数形式,我们提议并研究参数的最大可能性估计。我们使用超临界连续时间分流过程框架,证明这个估计符几乎可以肯定一致性和无症状的正常性。我们还提供了一个估计符,该估计符仅取决于网络的最后快照,并证明其一致性,以及一般条件下的无症状正常性。我们在小型模拟研究中将估计符的性能与非参数估计符作比较。