My course notes give the following definitions; could someone please verify that the last definition is non-standard? (I've spent all evening googling, and isn't "minimum cut" a concept related to cut sets rather than to edge cuts (all terms as defined below)? For example, see http://en.wikipedia.org/wiki/Minimum_cut and http://scientopia.org/blogs/goodmath/2007/08/07/maximum-flow-and-minimum-cut/.)
A cut set of a graph $G$ induced by a partition of $G$'s vertices into sets $X$ and $Y$ is the set of all edges with one endpoint in $X$ and another endpoint in $Y$.
An edge cut of a connected graph $G$ is a set $S$ of $G$'s edges such that $G$-$S$ is disconected and $G$-$S$' is connected for any proper subset $S$' of $S$.
A minimum cut of a graph $G$ is an edge cut of $G$ with the smallest-possible cardinality (called the edge connectivity of $G$).