Phase transition in the recoverability of network history

TL;DR

This paper introduces a Bayesian approach to network archaeology, revealing a phase transition in the ability to reconstruct network history, and demonstrates that meaningful inference is possible even in challenging scenarios.

Contribution

It presents a novel Bayesian formulation and efficient algorithms for network history reconstruction, identifying a phase transition in recoverability.

Findings

A phase transition exists in network history recoverability.

Nontrivial inference is feasible in many scenarios.

Algorithms perform well on artificial and real networks.

Abstract

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.