The vulnerability shows the resistance of the network until communication breakdown after the disruption of certain stations or communication links. This study introduces a new vulnerability parameter, neighbor rupture degree. The neighbor rupture degree of a non-complete connected graph \(G\) is defined to be
\[Nr(G) = \max\{w(G/S) – |S| – c(G/S): S \subset V(G), w(G/S) \geq 1\}\]
where \(S\) is any vertex subversion strategy of \(G\), \(w(G/S)\) is the number of connected components in \(G/S\), and \(c(G/S)\) is the maximum order of the components of \(G/S\). In this paper, the neighbor rupture degree of some classes of graphs are obtained and the relations between neighbor rupture degree and other parameters are determined.