During last decades, contingency analysis has been facing challenges from significant load demand increase and high penetrations of intermittent renewable energy, fluctuant responsive loads and non-linear power electronic interfaces. It requires an advanced approach for high-performance contingency analysis as a safeguard of the power system operation. In this paper, a graph-based method is employed for N-1 contingency analysis (CA) fast screening. At first, bi-directional breadth-first search (BFS) is proposed and adopted on graph model to detect the potential shedding component in contingency analysis. It implements hierarchical parallelism of the graph traverse and speedup its process. Then, the idea of evolving graph is introduced in this paper to improve computation performance. For each contingency scenario, N-1 contingency graph quickly derives from system graph in basic status, and parallelly analyzes each contingency scenario using graph computing. The efficiency and effectiveness of the proposed approach have been tested and verified by IEEE 118-bus system and a practical case SC 2645-bus system.