In this work, we propose a novel method for accurately estimating the node-to-node correspondence between two graphs. Given two graphs and their pairwise node similarity scores, our goal is to quantitatively measure the overall similarity-or the correspondence-between nodes that belong to different graphs. The proposed method is based on a Markov random walk model that performs a simultaneous random walk on two graphs. Unlike previous random walk models, the proposed random walker examines the neighboring nodes at each step and adjusts its mode of random walk, where it can switch between a simultaneous walk on both graphs and an individual walk on one of the two graphs. Based on extensive simulation results, we demonstrate that our random walk model yields better node correspondence scores that can more accurately identify nodes and edges that are conserved across graphs.