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Centrality measures are among the most fundamental tools for social network analysis. Since network data is often incomplete, erroneous, or otherwise manipulated, increasing attention has recently been paid to studying the sensitivity of centrality measures to such distortions. However, thus far no universal method of quantifying the manipulability of centrality measures has been proposed. To bridge this gap in the literature, we take an axiomatic approach. In particular, we introduce a set of intuitive axioms that characterize such a measure, and prove that there exists only one solution that satisfies them. Next, building upon this measure, we quantify the manipulability of the most fundamental centrality measures.

The Manipulability of Centrality Measures-An Axiomatic Approach