Give an example of a set of clusters in which merging based on the closeness of clusters leads to a more natural set of clusters than merging based on the strength of connection (interconnectedness) of clusters.

What will be an ideal response?

An example of this is given in the Chameleon paper that can be found at
http://www.cs.umn.edu/ karypis/publications/Papers/PDF/chameleon.pdf.
The example consists of two narrow rectangles of points that are side by side.
The top rectangle is split into two clusters, one much smaller than the other.
Even though the two rectangles on the top are close, they are not strongly
connected since the strong links between them are across a small area. On the
other hand, the largest rectangle on the top and the rectangle on the bottom
are strongly connected. Each individual connection is not as strong, because
these two rectangles are not as close, but there are more of them because
the area of connection is large. Thus, an approach based on connectivity will
merge the largest rectangle on top with the bottom rectangle.