A Metric for Measuring the Strength of Inter-dependencies

Abstract

We propose a metric for the analysis and estimation of the inter dependencies in networks of dynamic systems, formally defining the dependency among nodes and showing that the metric approximates the strength of the dependency. We propose a data driven metric based on known direct functional input/output relations among nodes, derived from the generic constitutive equations of the systems, giving a physical and rigorous meaning to the otherwise elusive word “dependency”. Our metric is also related to the input/output physical quantities, realizing a data driven approach discarding the internal node dynamics. This metric is particularly suited for the analysis of the Critical Infrastructures (CI) where typically a number of input/output measurements are available. It is vital for these CI, represented as technological networks, to characterize and to measure the inter-dependencies among their components in order to avoid destructive phenomena such as cascading failures. The proposed metric is algorithmically simple and can be used as a real-time tool. It was also shown how this approach is suited to the analysis of large technological networks.