  The betweenness centrality of graphs using random walk paths instead of
geodesics is studied. A scaling collapse with no adjustable parameters is
obtained as the graph size $N$ is varied; the scaling curve depends on the
graph model. A normalized random betweenness, that counts each walk passing
through a node only once, is also defined. It is argued to be more useful and
seen to have simpler scaling behavior. In particular, the probability for a
random walk on a preferential attachment graph to pass through the root node is
found to tend to unity as $N\rightarrow\infty.$
