Figure 8

Schematic of cutting strategies and spanning clusters. Leaves of the binary tree, e.g. domains, are numbered 1 to 12. In the figure, it is assumed that four clusters (1,2,3), (7, 8, 9) and (12) are from one particular fold and the three clusters (4, 5, 6), (10) and (11) contain all 5 domains of another fold. Horizontal line A – A represents the level cut, which produces a partition of 7 clusters but which splits the cluster (1,2,3) into two clusters, (1,2) and (3). Oblique line B – B is an allowable cut which produces a partition of 6 clusters and does not split (1,2) from (3). The node n1 represents the spanning cluster of the fold having domains 4, 5, 6, 10 and 11. The span, or size, of this spanning cluster is nine, and its excess span, or number of included domains not in this fold, is four. The node labelled n2, spanning three domains, namely 4, 5, and 6, represents the largest homogeneous cluster of this fold. For this fold, the relative size of the largest homogeneous cluster is 3/5, e.g. the size of the largest homogeneous cluster divided by the size of the associated fold.