Network archaeology: Phase transition in the recoverability of network history

Network archaeology: Phase transition in the recoverability of network history

Talk presented at NetSci 2018 (https://www.netsci2018.com/)

arXiv: https://arxiv.org/abs/1803.09191
Code: https://github.com/jg-you/network-archaeology

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 importance sampling algorithm to evaluate the posterior averages of this model, as well as an efficient heuristic that uncovers the history of a network in linear 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 non-trivial inference is possible in a large portion of the parameter space as well as on empirical data.

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Jean-Gabriel Young

June 13, 2018
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