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[[Image:Passing-constraint.svg|thumb|The constraint passed from node i to j summarizes the effects of nodes on the "side" of i affect j.]]
In a tree, every edge breaks the graph in two parts. The constraint passed along an edge tells how the part of the originating end of the edge affects the variables of the destination node. In other words, a constraint passed from node <math>i</math> to node <math>j</math> tells how the nodes "on the side of <math>i</math>" constrain the variables of node <math>j</math>.
If the variables of these two nodes are <math>X_i</math> and <math>X_j</math>, the nodes on the size of <math>i</math> do not affect all variables <math>X_j</math> but only the shared variables <math>X_i \cap X_j</math>. As a result, the influence on <math>X_j</math> of the nodes on the side of <math>i</math> can be represented as a constraint on variables <math>X_i \cap X_j</math>. Such a constraint can be seen as a "summary" of how a set of nodes affects another node.
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