A psychological network analysis of the relationship among component importance measures

Importance measures (IMs) in networks are indices that allow the analysis and evaluation of the network components that are most critical to the performance of the network. Such information is useful for a decision-maker as it enables taking actions to prevent or improve the performance of the network in the face of changing operational events (e.g., the identification of important links that should be hardened or made redundant). This paper presents an approach to analyze the relationships between the IMs through the use of so-called psychological networks, which estimate the characteristics of a new kind of network wherein the "nodes" correspond to IMs and the connecting links and their capacities are derived statistically using the IMs calculated. Such estimation does not use any a priori information of relationships among IMs. The approach proposed in this work defines an equivalence paradigm not described previously in the literature between the approach used in psychology and the IMs used to measure networks. As a result, the main characteristics of the relationships among IMs are derived, such as magnitude, sign, and robustness of the selected IMs. An example related to a transportation network and a set of flow-based IMs illustrates the contribution of psychological networks for understanding how the IMs interact.