= Solution
{c}
\b[It is <single-linkage clustering>.] Its intercluster distance is the smallest cross-pair <Euclidean distance>. Successive nearby points can join around the ring and within the dense central cloud before any edge crosses the gap between them. Equivalently, at a threshold below the between-group gap but above the lengths needed to connect each group, the <single-linkage clustering> components are precisely the central group and the ring.
<Complete-linkage clustering> uses the largest cross-pair <Euclidean distance>. Opposite points on the ring are far apart, so an intact ring has a large <diameter>. That rule favors compact pieces and can attach a ring segment to the center before all ring segments join. The visible gap and short links within each group explain why <single-linkage clustering> recovers the two intended <clusters in cluster analysis> in this example; it is not a universal guarantee for arbitrary noisy rings.
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