Fig. 4

Network N^u on labelset X = {1,2,3,4} and the simple graph resulting from the leaf shrinking procedure, which is an edge. At first, leaves 1,2,3 and 4 are deleted, resulting in a graph with one new leaf without label (cf. Fig. 2). Then, this new leaf is removed as well, which results in a triangle. Now, one vertex of degree 2 is suppressed and the parallel edge is deleted resulting in one single edge. Thus, N^u is called edge-based. Note that this graph resulting from the leaf shrinking procedure differs from the graph resulting from the leaf cutting procedure depicted in Fig. 2