Fig. 2

An example illustrating that different weighting schemes prefer different motif cuts: the four triangles have mean-weights of 2, 1, \(\frac {5}{3}\) and \(\frac {5}{3}\), and product-weights of 6, 1, 3 and 3 respectively whereas the minimum edge weight in each triangle is 1. Thus, the minimum formulation cannot distinguish between the cuts, whereas, under the mean formulation Cut 1 gives a cut of size 9, and Cut 2 gives a cut of size 10. On the other hand, under the product formulation, Cut 1 gives a cut of size 7, and Cut 2 gives a cut of size 6. Hence the mean formulation prefers Cut 1 and product formulation prefers Cut 2