Comparative Theoretical Analysis of Medial Centrality Measures

We study medial centrality measures that assess the role of a node in connecting others in the network. We focus on a setting with one target node t and several source nodes. We consider four classic measures adapted to this setting: Betweenness Centrality, Stress Centrality, Random Walk Betweenness Centrality and PageRank. While Betweenness and Stress Centralities assume that the information in the network follows the shortest path, Random Walk Betweenness Centrality and PageRank assume it moves randomly along the edges. We develop the axiomatic characterizations of all four measures. Our analysis shows that, while conceptually different, all four measures share several common properties.