Influence of measurement errors on networks: Estimating the robustness of centrality measures

Abstract

Most network studies rely on a measured 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. Previous studies have dealt either with the general effects of measurement errors on centrality measures or with the treatment of erroneous network data. In this paper, we propose a method for estimating the impact of measurement errors on the reliability of a centrality measure, given the measured network and assumptions about the type and intensity of the measurement error. This method allows researchers to estimate the robustness of a centrality measure in a specific network and can, therefore, be used as a basis for decision-making. In our experiments, we apply this method to random graphs and real-world networks. We observe that our estimation is, in the vast majority of cases, a good approximation for the robustness of centrality measures. Beyond this, we propose a heuristic to decide whether the estimation procedure should be used. We analyze, for certain networks, why the eigenvector centrality is less robust than, among others, the pagerank. Finally, we give recommendations on how our findings can be applied to future network studies.

Immunization strategies in networks with missing data

“…Second, missing data can affect the measurement of network properties, like degree and betweenness [34]. The rank order of nodes (from least to most important) may deviate from the true rank order on the complete, but unknown, network [51,52]. Thus, among the set of nodes that can be immunized (i.e., those who actually participate) one runs the risk of picking a sub-optimal target set to be immunized.…”

Sensitivity analysis for network observations with applications to inferences of social influence effects

“…Future research may explore the analytical solutions of the sensitivity analysis as applied to other network outcome (e.g. centrality (Martin & Niemeyer, 2019)) and influence models. 3.…”

“…In this context, our proposed methods can contribute to questions such as how inference about social influence effects is robust to errors/bias in networks generated by various mechanisms (e.g., homophily). (3) While how network errors affect other outcomes (e.g., centrality) have been studied (Martin & Niemeyer, 2019), the robustness of social influence effect to network errors is less explored. As outcomes and identification of social influence effects are critically contingent upon the network structure or to whom individuals are exposed (Friedkin & Johnsen, 1999), it is vital to investigate how inference of social influence effects is robust to alternatives or possible errors in the measurement of network ties.…”

On the impact of network size and average degree on the robustness of centrality measures

“…The error mechanisms that remove edges degree (e-(p)) is an example of a nontrivial error mechanism, since the probability of an edge being affected depends on the position of that edge. For a more detailed discussion of the error mechanisms as random graphs, see Martin & Niemeyer (2019).…”

“…1 Previous studies have used the Pearson correlation to measure the robustness (Bolland, 1988;Costenbader & Valente, 2003;Borgatti et al, 2006). Like most recent studies, we use a rank correlation (Kim & Jeong, 2007;Wang et al, 2012;Holzmann et al, 2019;Martin & Niemeyer, 2019). The effects of errors on the robustness of centrality measures depend on several variables, for example, the type of centrality measure, the type and extent of the error, the network topology (e.g., tree-like, core-periphery), and how we measure the robustness (Frantz et al, 2009;Smith & Moody, 2013).…”