Everyone has exactly one best friend.
Let me define few predicates before proceeding to the answer :
$F(x,y)$ = $y$ is a Best friend of $x$. And let the domain be All People in the world.
(Assuming that No one is a best friend of himself/herself. (i.e. $F(x,x)$ is False) )
$\forall x (\exists y F(x,y) \wedge \forall z ((z \neq y) \rightarrow \sim F(x,z)))$
Interpretation : For every person $x$ there is some person $y$ who is best friend of $x$ And for any(every) person $z$, if $z$ is not same person as $y$ then $z$ is Not a best friend of $x$.
Refer here for clarity about Uniqueness Quantifier/Quantification : https://gateoverflow.in/219473/kenneth-rosen-ch-1-ex-1-5-qn-52?show=219480#a219480