Network formation models explain the dynamics of the structure of connections using mechanisms that operate under different principles for establishing and removing edges. The Jackson-Rogers model is a generic framework that applies the principle of triadic closure to growing networks. Past work describes the asymptotic behavior of the degree distribution based on a continuous-time approximation. Here, we introduce a discrete-time approach that provides a more accurate fit of the dynamics of the in-degree distribution of the Jackson-Rogers model. Furthermore, we characterize the limit distribution and the expected value of the average degree as equilibria, and prove that both equilibria are asymptotically stable.