[1] The girth of other classes of matroids also corresponds to important combinatorial problems.
For instance, the girth of a co-graphic matroid (or the cogirth of a graphic matroid) equals the edge connectivity of the underlying graph, the number of edges in a minimum cut of the graph.
[2] Any set of points in Euclidean space gives rise to a real linear matroid by interpreting the Cartesian coordinates of the points as the vectors of a matroid representation.
The girth of the resulting matroid equals one plus the dimension of the space when the underlying set of point is in general position, and is smaller otherwise.
Girths of real linear matroids also arise in compressed sensing, where the same concept is referred to as the spark of a matrix.