A detailed analysis of convergence rate is presented for an iterative path formulated optimal routing algorithm. In particular, it is quantified, analytically, how the convergence rate changes as the number of nodes in the underlying graph increases. The analysis is motivated by a particular path formulated gradient projection algorithm that has demonstrated excellent convergence rate properties through extensive numerical studies. The analytical result proven in this note is that the number of iterations for convergence depends on the number of nodes only through the network diameter.