This paper presents the contingency ranking methodology of large interconnected power system for low frequency oscillatory instability problems. The oscillatory instability leading to blackout is often triggered by contingencies, such as line outage. In literatures, so far there is no such methodology presented for contingency ranking related to low frequency oscillatory instability. Two methodologies, namely, Hopf Bifurcation (HB) and Improved Hopf Bifurcation Indices, are proposed in this paper for contingency ranking. Hopf bifurcation, which describes the onset of an oscillatory problem, is detected by calculating minimum singular value of modified reduced system state or extended system matrices. The normalized minimum singular value or linearized minimum singular value is then used to rank the contingencies. The effectiveness of the methodology is tested and validated on 16 machine 68 bus test system.