Reliability assessment is crucial when dealing with complex systems, especially complex networks. Be they natural or man made, networks are able to sustain their functioning by means of a reliable set of components. The many functions a network can sustain are direct consequence of the topological structure that constraints and, at the same time, defines, the dynamical relation between its components. Therefore, some kind of relation between structure and dynamics should be expected to appear. In this paper, some of these relations that have been found for the European power grid are presented. Evidences for a critical relation between topology and dynamics are summarized, using some basic topological measures widely used in the developing complex networks paradigm. Finally, strategies for optimal management and operation of such networks are suggested.