This paper investigates random walks on complex networks and derives an exact expression for the mean first passage time (MFPT) between two nodes. The random walk centrality $ C $, defined as the ratio of a node's coordination number to its characteristic relaxation time, determines the MFPT. Nodes with higher $ C $ values are more efficient in receiving and spreading information. Numerical simulations on network models confirm this analytical result. Random walks are fundamental dynamic processes on networks and are important for transport and search. The MFPT is an important characteristic of random walks, and the paper derives an exact formula for the MFPT between two nodes. The difference in MFPT between two directions is determined by the random walk centrality $ C $, which links structural heterogeneity to dynamic asymmetry. The paper considers an arbitrary finite network and derives the master equation for the probability of a random walker moving between nodes. The stationary distribution of the walker is proportional to the degree of the node. The MFPT is calculated using the Laplace transform of the first-passage probability. The result shows that the average return time does not depend on the network's global structure but is determined by the node's degree and total number of links. The random walk centrality $ C $ is defined as the ratio of the stationary distribution to the characteristic relaxation time. It quantifies how central a node is in terms of its ability to receive and spread information. In scale-free networks, $ C $ is roughly proportional to the node's degree, but not monotonically due to variations in relaxation time. The paper also presents numerical simulations on the Barabási-Albert and hierarchical networks, showing that nodes with higher $ C $ values are visited earlier by random walkers. This implies that information is centralized in nodes with higher $ C $ values, which can lead to congestion in information transport processes. The results suggest that nodes with high $ C $ values should be carefully managed in network design. The study focuses on undirected networks, and future work could explore directed networks and interactions among multiple random walkers.This paper investigates random walks on complex networks and derives an exact expression for the mean first passage time (MFPT) between two nodes. The random walk centrality $ C $, defined as the ratio of a node's coordination number to its characteristic relaxation time, determines the MFPT. Nodes with higher $ C $ values are more efficient in receiving and spreading information. Numerical simulations on network models confirm this analytical result. Random walks are fundamental dynamic processes on networks and are important for transport and search. The MFPT is an important characteristic of random walks, and the paper derives an exact formula for the MFPT between two nodes. The difference in MFPT between two directions is determined by the random walk centrality $ C $, which links structural heterogeneity to dynamic asymmetry. The paper considers an arbitrary finite network and derives the master equation for the probability of a random walker moving between nodes. The stationary distribution of the walker is proportional to the degree of the node. The MFPT is calculated using the Laplace transform of the first-passage probability. The result shows that the average return time does not depend on the network's global structure but is determined by the node's degree and total number of links. The random walk centrality $ C $ is defined as the ratio of the stationary distribution to the characteristic relaxation time. It quantifies how central a node is in terms of its ability to receive and spread information. In scale-free networks, $ C $ is roughly proportional to the node's degree, but not monotonically due to variations in relaxation time. The paper also presents numerical simulations on the Barabási-Albert and hierarchical networks, showing that nodes with higher $ C $ values are visited earlier by random walkers. This implies that information is centralized in nodes with higher $ C $ values, which can lead to congestion in information transport processes. The results suggest that nodes with high $ C $ values should be carefully managed in network design. The study focuses on undirected networks, and future work could explore directed networks and interactions among multiple random walkers.