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

Abstract

Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and Erdős–Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.

Scientific Collaboration Network Views: A Brazilian Computer Science Graduate Programs Case

“…A low average degree may denote many isolated nodes, while, a high degree tells that there are many relationships among nodes (i.e., high collaboration). Although there are no conclusive studies, in [Martin and Niemeyer 2021] the authors present empirical evidence demonstrating that average degree can explain the robustness of networks regardless of their sizes. Specifically, they tested that average degree is a more robust centrality measure when compared to Eigenvector and PageRank, even considering different levels of errors (e.g., duplicated nodes, erroneous removal of nodes or vertices).…”

Introduction to the special issue on COMPLEX NETWORKS 2019

“…In Martin and Niemeyer (2020), the authors investigate how different kinds of mismeasurements affect centrality measures. Robustness is measured by injecting errors through an error mechanism that emulates some possible data errors: edge addition, uniform and degreeproportional edges removal, nodes removal.…”