Estimating the sensitivity of centrality measures w.r.t. measurement errors

Most network studies rely on an observed network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics, especially on centrality measures: a more central node in the observed network might be less central in the underlying network. We introduce a metric for the reliability of centrality measures -- called sensitivity. Given two randomly chosen nodes, the sensitivity means the probability that the more central node in the observed network is also more central in the underlying network. The sensitivity concept relies on the underlying network which is usually not accessible. Therefore, we propose two methods to approximate the sensitivity. The iterative method, which simulates possible underlying networks for the estimation and the imputation method, which uses the sensitivity of the observed network for the estimation. Both methods rely on the observed network and assumptions about the underlying type of measurement error (e.g., the percentage of missing edges or nodes). Our experiments on real-world networks and random graphs show that the iterative method performs well in many cases. In contrast, the imputation method does not yield useful estimations for networks other than Erd\H{o}s-R\'enyi graphs.