Accurately assessing the vulnerability of network systems is vital for network security planning and risk management. Existing network vulnerability analysis methods mostly focus on identifying vulnerable elements with a single feature. With the quickening of network system complexity process, the diversified vulnerability identification is particularly important. This paper innovatively proposes a vulnerability analysis method for critical elements based on network connectivity from the perspective of attackers, identifying network elements with multiple important identities and low-disruption-cost. Critical elements are identified by using local analysis measures, network connectivity is used as the measure of vulnerability to identify the minimum-cost set of critical elements that can cause a particular degradation of network connectivity. The simulation results show that the proposed scheme is more accurate in locating vulnerable elements and can provide an effective and reliable reference for the development of protection measures.