A059687 - Basic Circuits = 3-conn cubic graphs ?

[Gordon Royle]

A059687 lists "basic circuits of nullity n".

What is a basic circuit of nullity n?

I ask because the numbers start 1, 1, 1, 2, 4, 14, 57 (in fact this is all
of them).

These are the numbers of 3-connected cubic graphs on 2, 4, 6, 8, 10, 12 and
14 vertices [I am cheating a bit with 2 vertices, but if I allow 3 edges in
parallel between the 2 vertices, then it works out].


So, are these two concepts the same?