Is there always a direct connection between the central nodes in an (undirected graph)?

Question

This link contains an examples about the graph central nodes, I noticed that if there are more than one central node in a graph G, then a they are always adjacent nodes (means there is a direct link between them)

Also, here is an example that illustrates the one and two central nodes

Answer 1

Check counterexample:

   *
   |
   *
  / \
 /   \
A     B
 \   /
  \ /
   *
   |
   *