Shaking Hands Dilemma Proof
Theorem 1
In any directed graph, the sum of the in-degrees and the sum of the out-degrees are equal.
Explanation
The handshake dilemma can be considered the handshake lemma for directed graphs.
Proof
In a directed graph, the sum of the out-degrees is equal to the number of arcs. Since an arc comes out from one vertex and enters another, the sum of the out-degrees and in-degrees are equal.
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Wilson. (1970). Introduction to Graph Theory: p105. ↩︎