Betweenness versus Linerank

Balázs Kósa, Márton Balassi, Péter Englert, Attila Kiss

In our paper we compare two centrality measures of networks, betweenness and Linerank. Betweenness is widely used, however, its computation is expensive for large networks. Calculating Linerank remains manageable even for graphs of billion nodes, it was offered as a substitute of betweenness in [12]. To the best of our knowledge the relationship between these measures has never been seriously examined. We calculate the Pearson’s and Spearman’s correlation coefficients for both node and edge variants of these measures. For edges the correlation tends to be rather low. Our tests with the Girvan-Newman algorithm [16] also underline that edge betweenness cannot be substituted with edge Linerank. The results for the node variants are more promising. The correlation coefficients are close to 1. Notwithstanding, the practical application in which the robustness of social and web graphs is examined node betweenness still outperforms node Linerank. We also clarify how Linerank should be computed on undirected graphs.