  Let $M$ be a Puiseux monoid, that is, a monoid consisting of nonnegative
rationals (under addition). A nonzero element of $M$ is called an atom if its
only decomposition as a sum of two elements in $M$ is the trivial decomposition
(i.e., one of the summands is $0$), while a nonzero element $b \in M$ is called
atomic if it can be expressed as a sum of finitely many atoms allowing
repetitions: this formal sum of atoms is called an (additive) factorization of
$b$. The monoid $M$ is called atomic if every nonzero element of $M$ is atomic.
In this paper, we study factorizations in atomic Puiseux monoids through the
lens of their associated Betti graphs. The Betti graph of $b \in M$ is the
graph whose vertices are the factorizations of $b$ with edges between
factorizations that share at least one atom. Betti graphs have been useful in
the literature to understand several factorization invariants in the more
general class of atomic monoids.
