  Sidorenko's Conjecture says that the minimum density of a bigraph $G$ in a
bigraphon $W$ of a given edge density is attained when $W$ is a constant
function. A consequence of a result by B. Szegedy is that it is enough to show
Sidorenko's Conjecture under the further assumption that $W$ is biregular. In
this paper, we retrieve this result with a more elementary proof. With this
biregularity result and some ideas of its proof, we also obtain simple proofs
of several other results related to Sidorenko's Conjecture. Furthermore, we
also show that bigraphs that have a special type of tree decomposition, called
reflective tree decomposition, satisfy Sidorenko's conjecture. This both
unifies and generalizes the notions of strong tree decompositions and
$N$-decompositions from the literature.
