Estimation of the Branching Factor in Noisy Networks

An important metric in understanding the dynamics on networks is the branching factor, which captures a sense of dispersion in the network connectivity and quantifies the rate of spreading across the network. Moreover, network information generally is available only up to some level of error. In this paper, we discuss the branching factor in the context of network epidemiology. We study the propagation of such errors to the estimation of the branching factor. Specifically, we characterize the impact of network noise on the bias and variance of the observed branching factor for arbitrary true networks, with examples in sparse, dense, homogeneous and inhomogeneous networks. Under some assumptions, we show that the observed branching factor is asymptotically unbiased in the homogeneous network setting, but asymptotically biased in the inhomogeneous network setting. In addition, we propose a method-of-moments estimator for the true branching factor. We illustrate the practical performance of our estimator through simulation studies and with contact networks observed in British secondary schools and a French hospital.