weinberg: chap 4 "Cluster decomposition principle"

hi,
   Was going thru weinberg, "Quantum theory of fields" 
chap 4 "The cluster decomposition principle".
In section 4.4 "structure of interaction" he gives a proof, that if
h_{NM} has only single delta funtion, then it guarantees that the S-matrix
satisfies the cluster decomposition principle.
   Basically, he draws a graph which depicts the movement of the 
annihilation operators across the creation operators. Now, I havent
got the physical intuition as to why he draws the graph the way he draws.
Can someone out there help me out on this??

ganesh