Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: reconstructing all the past states of a network from its structure—a difficult permutation inference problem. In this paper, we introduce a Bayesian formulation of network archaeology, with a generalization of preferential attachment as our generative mechanism. We develop a sequential Monte Carlo algorithm to evaluate the posterior averages of this model, as well as an efficient heuristic that uncovers a history well correlated with the true one, in polynomial time. We use these methods to identify and characterize a phase transition in the quality of the reconstructed history, when they are applied to artificial networks generated by the model itself. Despite the existence of a no-recovery phase, we find that nontrivial inference is possible in a large portion of the parameter space as well as on empirical data.

中文翻译：

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网络历史记录可恢复性中的相变

网络增长过程可以理解为复杂网络的结构和历史的生成模型。这种观点自然导致了网络考古学的问题：从网络的结构重建网络的所有过去状态，这是一个困难的排列推理问题。在本文中，我们介绍了网络考古学的贝叶斯表述，将优先依附性概括为我们的生成机制。我们开发了一种顺序蒙特卡罗算法来评估该模型的后验平均值，以及一种有效的启发式算法，该算法可在多项式时间内揭示与真实值很好相关的历史记录。当将这些方法应用于模型本身生成的人工网络时，我们将使用这些方法来识别和表征重建历史的质量。