  A model of the Italian 380 kV electrical transmission network has been
analyzed under the topological and the functional viewpoints. The DC power flow
model used to evaluate the power flux has been solved on the basis of input
conditions (injected power - extracted power, line's reactances and the maximum
flux capacity of each line) taken from real data. The vulnerability of the
network under load conditions has been estimated by evaluating the power flux
redistribution along the lines subsequent to line's removal. When the perturbed
network cannot sustain a given input--output demand, the maximum power
sustainable by the network has been evaluated to optimize the \texttt{Quality
of Service}, defined as the difference between the expected and the effective
dispatched power. The functional relevance of the different lines of the
network has been classified according to the amount of power that the network
must reduce, to keep alive, upon their removal. Results show that topological
and functional relevances are related to different lines; lines having a strong
topological relevance may have a bare relevance in the flow distribution and
thus their removal does not affect the functioning of the network.
