# Handshake Lemma

DevFeed: [Handshake Lemma](<https://devfeed.tech/articles/handshake-lemma-40258.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/01/29/handshake-lemma/>)

Published: 2012-01-29T22:24:31Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Graphs](<https://devfeed.tech/topics/graphs.md>), [graph theory](<https://devfeed.tech/topics/graph-theory.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>)

Tags: [graph](<https://devfeed.tech/tags/graph.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [handshake](<https://devfeed.tech/tags/handshake.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>)

## AI overview

The article proves the Handshake Lemma: in a party of n people, the number of people with an odd number of friends must be even. It uses double-counting to show that the sum of all friendship counts equals twice the total number of friendships, and then relates the result to graph theory.

## Source excerpt

Problem: Prove or disprove: at a party of $ n$ people, there must be an even number of people who have an odd number of friends at the party. Solution: Let $ P$ be the set of all people, and for any person $ p \in P$, let $ d(p)$ be the number of friends that person has. Let $ f$ be the total number of friendships between pairs of people at the party.