One of the key issues in designing network topology is vulnerability. A vulnerability parameter measures the resistance of a network to disruption of operation after the failure of certain stations or communication links. One measure of the vulnerability of a network is the edge connectivity. A more selective concept of edge-connectivity is introduced, called the k - component order edge-connectivity that will be introduced in designing for MAN topology. This parameter equals the smallest number of edges that must be removed in order to ensure that the order of each component of the resulting sub-network or sub-graph is less than k.