Title: Estimating the sensitivity of centrality measures w.r.t. measurement errors,
Abstract: 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
Erdős-Rényi graphs.