关键词: 网络, 可靠性, 影响度, 最小点割, 连通度

Abstract: Connectivity is not only an index to evaluate the status of network connectivity and survivability，but also an important feature of the network structure.Regarding the deficiency of the present algorithm for solving the connectivity of networks，which needs to change existing network to capacity network，a new algorithm is proposed in this paper，basing on inspiration of the paralysis of transportation network.By introducing two influencing degree-vector to stress the importance of the point in network，it shows that the new algorithm can not only solve network connectivity and determine the minimum vertex-cut，but also simple and easy to implement.Finally，the effectiveness is proved through simulation experiment and example.

Key words: networks, invulnerability, influence, minimum vertex-cut, connectivity