prove that any self complementary graph is connected

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I have already shown that if a graph G=(V,E) is self complementary then we must have |V|=4k or |V|=4k+1 for some positive integer k, but now I am struggling to find a way to show that every self complementary graph is connected. Any help would be appreciated, thank you.

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It is a famous observation of Erdös that a graph or its compliment must be connected. Confirm this and use this for your problem.