Baker and Norine initiated the study of graph divisors as a graph-theoretic analogue of the Riemann-Roch theory for Riemann surfaces. One of the key concepts of graph divisor theory is the rank. The study of graph divisors has been a rapidly developing field in recent years, with many new results and applications emerging. In this research activity, we aim to explore the properties and behavior of graph divisors, particularly in relation to their rank. We will investigate the conditions under which the rank of a graph divisor can be approximated, and explore the implications of these results for the study of graph divisors.