Fig. 2

Illustration of the gNNI operation on labeled trees. A On a unrooted labeled tree, a gNNI operation on an edge (a, b) interchanges one or more children of a with an arbitrary number of children of b. B On a rooted labeled tree, a gNNI operation on an edge (a, b) (where b is the child of a) not only rewires the selected edges leaving a and b (left), but also rewires the unique edge entering a and b simultaneously if necessary (right).