For instance, a graph is -tough if the number of components formed by removing a set of vertices is always at most as large as the number of removed vertices. The toughness of a graph is the maximum  for which it is -tough; this is a finite number for all finite graphs except the complete graphs, which by convention have infinite toughness.
For instance, a graph is considered robust if the number of separate subgraphs created by deleting a set of vertices is always less than or equal to the size of that deleted group. The robustness of a graph refers to the maximum value for which it remains robust; this figure exists for all finite graphs except the fully connected ones, which are conventionally assigned infinite robustness.