Open Access

Network analysis methods have long been used in the social sciences. About 25 years ago, these methods gained popularity in various other domains and many real-world phenomena have been modeled using networks. Well-known examples include (online) social networks, economic networks, web graphs, metabolic networks, infrastructure networks, and many more. Technological development made it possible to store and process data on a scale not imaginable decades ago — a development that also includes network data. A particular characteristic of network data is that, unlike standard data, the objects of interest, called nodes, have relationships to (possibly all) other objects in the network. Collecting empirical data is often complicated and cumbersome, hence, the observed data are typically incomplete and might also contain other types of errors. Because of the interdependent structure of network data, these errors have a severe impact on network analysis methods. This cumulative dissertation is about the impact of erroneous network data on centrality measures, which are methods to assess the position of an object, for example a person, with respect to all other objects in a network. Existing studies have shown that even small errors can substantially alter these positions. The impact of errors on centrality measures is typically quantified using a concept called robustness. The articles included in this dissertation contribute to a better understanding of the robustness of centrality measures in several aspects. It is argued why the robustness needs to be estimated and a new method is proposed. This method allows researchers to estimate the robustness of a centrality measure in a specific network and can be used as a basis for decision making. The relationship between network properties and the robustness of centrality measures is analyzed. Experimental and analytical approaches show that centrality measures are often more robust in networks with a larger average degree. The study of the impact of non-random errors on the robustness suggests that centrality measures are often more robust if missing nodes are more likely to belong to the same community compared to missingness completely at random. For the development of imputation procedures based on machine learning techniques, a process for the evaluation of node embedding methods is proposed.