The Manipulability of Centrality Measures-An Axiomatic Approach

Centrality measures—methods for evaluating the nodes’ relative positions and roles in the network—are among the most fundamental tools in social network analysis [25]. One of the issues that attracted attention in the literature is the sensitivity of centrality measures [8, 13]. This interest is driven by the fact that real-life data about the links in a network are often incomplete, erroneous, or otherwise distorted [17]. There are various reasons behind this, many of which are unintentional, such as the under-reporting of network relationships [28](eg, there are many real-life relationships that are not declared on Facebook) or the errors made by informants while asked about their ties [15]. The studies that evaluate the effects of such random distortions typically assume that only a certain