In previous literature Coykendall & Maney, as well as Axtell & Stickles, have discussed the concept of irreducible divisor graphs of elements in domains and ring with zero-divisors respectively, with two different definitions. In this paper we seek to look at the irreducible divisor graphs of ring elements under a hybrid definition of the two previous ones—in hopes that this graph will reveal structure concerning irreducible divisors in rings with zero-divisors. We also compare the three graphs and examine in what respects they are related. Other graph-theoretic properties of this graph will also be discussed.