  We study the connected correlator of 1/2 BPS winding Wilson loops in
$\mathcal{N}=4$ $U(N)$ super Yang-Mills theory, where those Wilson loops are on
top of each other along the same circle. We find the exact finite $N$
expression of the connected correlator of such Wilson loops. We show that the
$1/N$ expansion of this exact result is reproduced from the topological
recursion of Gaussian matrix model. We also study the exact finite $N$
expression of the generating function of 1/2 BPS Wilson loops in the symmetric
representation.
