Running intersection property
= Running intersection property
{title2=$C_i\cap C_j\subseteq C_k\quad\text{along the path from }i\text{ to }j$}
The running intersection property says that every variable belongs to a connected subtree of a <junction tree>. Equivalently, every clique along the path between two cliques contains their intersection. This ensures that eliminating variables on one side of a tree edge leaves a message depending only on its separator with the other side.