Deriving a minimum set of indicators to assess network component importance

The importance of the components of a system has been widely studied in the literature. The main objective of such component importance measures (CIMs) is to evaluate the effect that the components can cause in the system under study by not being present or to quantify the participation of their presence in functional characteristics of the system. When dealing with several CIMs that represent different perspectives on importance, different CIMs can produce different rankings of importance. To detect the possible existence of a minimum set of indicators useful for assessing the importance of the components, this work proposes an innovative two-step procedure, which we apply to networks. In the first step, a set of similar functional networks is proposed as evaluators or "judges" for determining the set of CIMs that provide the most information on the importance of the components. And in the second step, a multi-criteria decision analysis technique is adopted to rank the CIMs. The proposed approach is illustrated for (i) a set of CIMs and (ii) a set of 13 different electric power networks.