Let R be an integral domain, and let x ∈ R be a nonzero nonunit that can be written as a product of irreducibles. In [3], the author and J. Coykendall defined the irreducible divisor graph of x, denoted G(x), as follows. The vertices of G(x) are the nonassociate irreducible divisors of x (each from a pre-chosen coset of the form πU (R) for π ∈ R irreducible). Given distinct vertices y and z, we put an edge between y and z if and only if yz|x. Finally, if y n |x but y n+1 x, then we put n − 1

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... ps on the vertex y. In this paper, inspired by the approach of the authors from [1], we study G(x) using homology. A connection is found between H 1 and the cycle space of G(x). We also characterize UFDs via these homology groups.