because in your example the nodes containing variable 1 are (1,2,3) and (1,4,5) and there is a path between them thru node (2,3,4) so they are **connected** in regular graph theory terminology, right?

e.g., see below for variable 1

(1,2,3) — (2,3,4) — (1,4,5)

The nodes containing 1 are disconnected.

]]>What do you mean by **"connected component"**? A junction tree is a spanning tree, and in a spanning tree every set of nodes are connected! did you mean **directly** connected?