Choosing the meshes in a circuit with a given tree
The rules are:


links = branches not part of the tree (i.e. the cotree)
each mesh = closed by taking exactly one link (rest is from the tree)


So if you take R1 as link you get the mesh along R1, R2, Uq2. Then if you take R3 as link you get R3, R2, Uq2, Uq1. Finally, if you take Uq3 as link, you get your last mesh which goes around the outer perimeter.