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The pomegranate tree is a symbol of friendship, childhood innocence, and shelter. When it appears in the first part of the story, Amir and Hassan were fast friends who, despite elements of caste, shared happy times together and enjoyed each other's company. The lush, blooming tree paralleled their lives which were full of promise, and its wide, spreading branches provided shelter, as did their comaraderie.
When Amir sees the tree again when he returns to his childhood home in the latter part of the story, it is bare and has ceased to blossom, like the ruins of his friendship with Hassan. All that remains of that idyllic time is a memory, as represented by the carvings they made on the tree as children.