where s, t and i are distinct nodes of the graph, s st is the total number of shortest paths between nodes s and t, and s st (i) is the number of those shortest paths that go through node i [38] . The random-walk centrality of a node i is a measure based on random walks, counting how often the node i is traversed by a random walk between any pair of nodes s and t. Following Newman [39] , we rank nodes according to the random-walk measure