Betweenness versus Linerank

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.</jats:p

Component Evolution Analysis in Descriptor Graphs for Descriptor Ranking

This paper presents a method based on graph behaviour analysis for the evaluation of descriptor graphs (applied to image/video datasets) for descriptor performance analysis and ranking. Starting from the Erd˝os-R´enyi model on uniform random graphs, the paper presents results of investigating random geometric graph behaviour in relation with the appearance of the giant component as a basis for ranking descriptors based on their clustering properties. We analyse the phase transition and the evolution of components in such graphs, and based on their behaviour, the corresponding descriptors are compared, ranked, and validated in retrieval tests. The goal is to build an evaluation framework where descriptors can be analysed for automatic feature selection