Why does single linkage create loose clusters when it uses smallest distance between two points?

Question

The definition of single linkage says: In single linkage method, the distance between two clusters is defined as the minimum distance between two data points in each cluster.

However, different articles on clustering contradicts the above statement. The single linkage will create very loose clusters. Hence, the intra clusters variance would be high.

When the distance between two points is low then clusters would be tight cluster and variance should be low. Can someone throw some light to understand how loose clusters with high variance are formed with single linkage.

Answer 1

For single linkage, one pair of points causes two clusters to be merged regardless of the shape of the clusters and regardless how distant other pairs are. For complete linkage, only clusters are merged for which all pairs are close.

Complete linkage will thus result in more compact clusters, whereas single linkage can follow "bridges" built by close by point sequences. It depends on the application which type of clusters are preferable.