Ranking-betweenness centrality
Ranking-betweenness centrality
evaluates the importance of nodes in urban networks by combining random-walk betweenness with an adapted PageRank algorithm (APA) [2]. Unlike classical random-walk betweenness, which assumes equal probability of starting a random walk from any node, ranking-betweenness centrality weights these random walks according to the APA-derived importance of each starting node.
Formally, the ranking-betweenness centrality of node \(i\), denoted \(c_{rb}(i)\), is defined as
\[
c_{rb}(i) = \sum_{s \neq t} π_s \, σ_{st}(i),
\]
where \(σ_{st}(i)\) is the expected fraction of random-walk paths from node \(s\) to node \(t\) that pass through node \(i\), and \(π_s\) is the APA-based starting probability of node \(s\). The APA probability scores are computed using an
adapted PageRank algorithm
, where the starting probabilities can be set according to external information about node relevance. If no such information is available, a uniform starting probability is used for all nodes, so that the random walks are unbiased with respect to their starting points.