  Finding central nodes is a fundamental problem in network analysis.
Betweenness centrality is a well-known measure which quantifies the importance
of a node based on the fraction of shortest paths going though it. Due to the
dynamic nature of many today's networks, algorithms that quickly update
centrality scores have become a necessity. For betweenness, several dynamic
algorithms have been proposed over the years, targeting different update types
(incremental- and decremental-only, fully-dynamic). In this paper we introduce
a new dynamic algorithm for updating betweenness centrality after an edge
insertion or an edge weight decrease. Our method is a combination of two
independent contributions: a faster algorithm for updating pairwise distances
as well as number of shortest paths, and a faster algorithm for updating
dependencies. Whereas the worst-case running time of our algorithm is the same
as recomputation, our techniques considerably reduce the number of operations
performed by existing dynamic betweenness algorithms.
