Vulnerability in Networks - A Survey

The analysis of vulnerability in networks generally involves some questionsabout how the underlying graph is connected. One is naturally interestedin studying the types of disruption in the network that maybe causedby failures of certain links or nodes. In terms of a graph, the concept ofconnectedness is used in different forms to study many of the measuresof vulnerability. When certain vertices or edges of a connected graphare deleted, one wants to know whether the remaining graph is stillconnected, and if so, what its vertex - or edge - connectivity is. If on theother hand, the graph is disconnected, the determination of the number ofits components or their orders is useful. Our purpose here is to describeand analyses the current status of the vulnerability measures, identify itsmore interesting variants, and suggest a most suitable measure ofvulnerability.