The relation between the position of mutations in Saccharomyces cerevisiae metabolic network and their lethality is the subject of this work. We represent the topology of the network by a directed graph: nodes are metabolites and arcs represent the reactions; a mutation corresponds to the removal of all the arcs referring to the deleted enzyme. Using publicly available knock-out data, we show that lethality corresponds to the lack of alternative paths in the perturbed network linking the nodes affected by the enzyme deletion. Such feature is at the basis of the recently recognized importance of 'marginal' arcs of metabolic networks.