In this work, we propose a multi-perspective framework of analysis of critical infrastructures (CIs) with respect to supply service, topology and controllability. The framework enables identifying the role of CI elements and quantifying the consequences of scenarios of multiple failures, with respect to the different perspectives considered. To present the analysis framework, a benchmark network representative of a real gas transmission network across several countries of the European Union (EU) is considered. The information extracted from such analysis can help us to identify the critical elements and how the properties of the network are affected by failures, and to propose corresponding improvements for CIs. The findings of this paper d...