In an original and very interesting paper (Satyanarayana and Wood [1]) concerning polygon-to-chain reductions in a stochastic network, a small inconsistency occurs in the proof of Theorem 1. In particular, this happens in cases where the whole set of ${\bf K}$-vertices lies in the remaining polygon. Such an example is the case of polygon type 5, where the appropriate note has been made by the authors for $|{\bf K}| = 2$. Analogous notes must also be made for polygon types 4, 6, and 7, when ${\bf K} = 2,3$, and 4, respectively. The correct transformations are given in Table 1 (note that dark vertices are ${\bf K}$-vertices).