document: k-Centralities : local approximations of global measures based on shortest paths A lot of centrality measures have been developed to analyze different aspects of importance . Some of the most popular centrality measures ( e.g. betweenness centrality , closeness centrality ) are based on the calculation of shortest paths . This characteristic limits the applicability of these measures for larger networks . In this article we elaborate on the idea of bounded-distance shortest paths calculations . We claim criteria for k-centrality measures and we introduce one algorithm for calculating both betweenness and closeness based centralities . We also present normalizations for these measures . We show that k-centrality measures are good approximations for the corresponding centrality measures by achieving a tremendous gain of calculation time and also having linear calculation complexity O ( n ) for networks with constant average degree . This allows researchers to approximate centrality measures based on shortest paths for networks with millions of nodes or with high frequency in dynamically changing networks .
doc_bio_tags: O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O