Resilience is meant as the capability of a networked infrastructure to provide its service even if some components fail: in this paper we focus on how resilience depends both on net-wide measures of connectivity and the role of a single component. This paper has two objectives: first to show how a set of global measures can be obtained using techniques from network theory, in particular how the spectral analysis of the adjacency and Laplacian matrices and a similarity measure based on Jensen-Shannon divergence allows us to obtain a characteriza-tion of global connectivity which is both mathematically sound and operational. Second, how a clustering method in the subspace spanned by the l smallest eigen-vectors of the Laplacian matrix allows us to identify the edges of the network whose failure breaks down the network. Even if most of the analysis can be applied to a generic networked infrastructure, specific references will be made to Water Distribution Networks (WDN).