This paper introduces a new measure of betweenness centrality based on random walks, which differs from the traditional shortest-path betweenness measure. The new measure accounts for all paths between nodes, not just the shortest ones, but still gives more weight to shorter paths. It is calculated by counting how often a node is traversed by a random walk between two other nodes. The measure is shown to be computationally feasible using matrix methods, with a worst-case time complexity of O((m+n)n²), making it comparable in computational demands to flow betweenness. The traditional shortest-path betweenness measure assumes that information spreads only along the shortest paths, which may not always be the case. The new measure is more realistic as it considers the random nature of information flow in many networks. It is shown to perform better in cases where non-geodesic paths are important, such as in the example network where vertex C, which is not on any shortest path, has a higher betweenness score than vertices A and B. The new measure is shown to be numerically equivalent to the current-flow betweenness measure, which is derived from electrical circuit theory. This equivalence is demonstrated by showing that both measures yield the same results when applied to the same network. The random-walk betweenness measure is particularly useful for identifying vertices of high centrality that do not lie on geodesic paths or maximum-flow cut-sets. The paper also discusses the relationship between random-walk betweenness and other centrality measures, such as degree and shortest-path betweenness. It shows that while random-walk betweenness is moderately correlated with degree and highly correlated with shortest-path betweenness, there are vertices with significantly different random-walk betweenness scores compared to their scores on other measures. These vertices are likely to be important in the spread of information or disease in a network. The paper provides examples of the application of the random-walk betweenness measure to various networks, including a network of intermarriage relations between 15th century Florentine families and a coauthorship network of scientists. The results show that the measure can effectively identify vertices of high centrality in these networks. The paper concludes that the random-walk betweenness measure is a valuable tool for analyzing network data, particularly in cases where information or disease spreads in a non-ideal manner.This paper introduces a new measure of betweenness centrality based on random walks, which differs from the traditional shortest-path betweenness measure. The new measure accounts for all paths between nodes, not just the shortest ones, but still gives more weight to shorter paths. It is calculated by counting how often a node is traversed by a random walk between two other nodes. The measure is shown to be computationally feasible using matrix methods, with a worst-case time complexity of O((m+n)n²), making it comparable in computational demands to flow betweenness. The traditional shortest-path betweenness measure assumes that information spreads only along the shortest paths, which may not always be the case. The new measure is more realistic as it considers the random nature of information flow in many networks. It is shown to perform better in cases where non-geodesic paths are important, such as in the example network where vertex C, which is not on any shortest path, has a higher betweenness score than vertices A and B. The new measure is shown to be numerically equivalent to the current-flow betweenness measure, which is derived from electrical circuit theory. This equivalence is demonstrated by showing that both measures yield the same results when applied to the same network. The random-walk betweenness measure is particularly useful for identifying vertices of high centrality that do not lie on geodesic paths or maximum-flow cut-sets. The paper also discusses the relationship between random-walk betweenness and other centrality measures, such as degree and shortest-path betweenness. It shows that while random-walk betweenness is moderately correlated with degree and highly correlated with shortest-path betweenness, there are vertices with significantly different random-walk betweenness scores compared to their scores on other measures. These vertices are likely to be important in the spread of information or disease in a network. The paper provides examples of the application of the random-walk betweenness measure to various networks, including a network of intermarriage relations between 15th century Florentine families and a coauthorship network of scientists. The results show that the measure can effectively identify vertices of high centrality in these networks. The paper concludes that the random-walk betweenness measure is a valuable tool for analyzing network data, particularly in cases where information or disease spreads in a non-ideal manner.