This paper is concerned with the study of observability in a structural framework. It turns out that the system is structurally observable if and only if the system is output connected and contains no contraction. We focus our attention on the observability preservation under sensor failure. We consider linear observable systems and we wonder if a given system remains observable in case of sensor failure. More precisely, we will characterize among the sensors those which are critical, i.e., which failure leads to observability loss, those which are useless for observability purpose and the set of those which are useful without being critical. Using a graph approach we classify the sensors with respect to their importance for output connection preservation, contraction avoidance and then observability preservation under sensor failure.