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We know that the complete graph has n(n-1)/2 edges and we want to find out n such that n(n-1)/2 greater or equal to 500.

Thus n(n-1) greater or equal to 1000.

Taking n=33, we have,

n(n-1)=33(33-1)=1056>1000.

Therefore required smallest integer is n=33.

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