In this paper, the novel quantitative assessment method based on local network dynamic measurements has been developed. Based on the topological energy function given by Bergen and Hill, a new style of stability criterion is suggested which is based on line measurement. The stability indices for lines, cutsets and power system according to features of transient energy in the lines is given, which not only provide reliable and accurate assessment of the transient stability of the power system, but can be used to assess the effect of lines and cutsets on the transient stability and identify the weak transmission segment. The examples are presented by simulation on the IEEE-39 buses test system.