Sensitivity of Diffusion Dynamics to Network Uncertainty

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Abstract

Simple diffusion processes on networks have been used to model, analyze and predict diverse phenomena such as spread of diseases, information and memes. More often than not, the underlying network data is noisy and sampled. This prompts the following natural question: how sensitive are the diffusion dynamics and subsequent conclusions to uncertainty in the network structure?



In this paper, we consider two popular diffusion models: Independent cascade (IC) model and Linear threshold (LT) model. We study how the expected number of vertices that are influenced/infected, for particular initial conditions, are affected by network perturbations. Through rigorous analysis under the assumption of a reasonable perturbation model we establish the following main results. (1) For the IC model, we characterize the sensitivity to network perturbation in terms of the critical probability for phase transition of the network. We find that the expected number of infections is quite stable, unless the transmission probability is close to the critical probability. (2) We show that the standard LT model with uniform edge weights is relatively stable under network perturbations. (3) We study these sensitivity questions using extensive simulations on diverse real world networks and find that our theoretical predictions for both models match the observations quite closely. (4) Experimentally, the transient behavior, i.e., the time series of the number of infections, in both models appears to be more sensitive to network perturbations.

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