Fig. 5.

Toy example illustrating clustering. A: hypothetical points are scattered in a structured fashion on a 2-dimensional canvas. Clustering aims to recover the underlying structure. B: example solutions for M = 2, 3, 4, or 5 clusters are shown. The solutions for M = 2 or 5 clusters agree with visual assessment of the underlying structure and are therefore useful representations. On the other hand, seeking 3 or 4 clusters does not lead to satisfying solutions because solutions are ambiguous. For example, the M = 3 solution is not unique in the sense that an “equally good” alternate solution is for one group of points in the red cluster to be grouped with the orange cluster. Seeking M = 3 or 4 clusters is therefore unstable in the sense that different random initializations of the clustering algorithm lead to different “equally good” solutions. In the present study we employed a stability analysis to estimate the numbers of clusters and also examined both a relatively coarse solution (7 networks) and a fine-resolution solution (17 networks) to survey the solution space broadly (see Fig. 6).