Abstract
Networks have an important place in our daily lives. Internet networks, electricity networks, water networks, transportation networks, social networks and biological networks are some of the networks we run into every aspects of our lives. A network consists of centers connected by links. A network is represented when centers and connections modelled by vertices and edges, respectively. In consequence of the failure of some centers or connection lines, measurement of the resistance of the network until the communication interrupted is called vulnerability of the network. In this study, neighbor rupture degree which is a parameter that explores the vulnerability values of the resulting graphs due to the failure of some centers of a communication network and its neighboring centers becoming nonfunctional were applied to some middle graphs and neighbor rupture degree of the $M(C_{n}),$ $M(P_{n}),$ $M(K_{1,n}),$ $M(W_{n}),$ $M(P_{n}\\times K_{2})$ and $M(C_{n}\\times K_{2})$ have been found.