Abstract: Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The |$k$|-betweenness centrality of a vertex is defined similarly, but only considers shortest paths of length at most |$k$|. The sequence of |$k$|-betweenness centralities for all possible values of |$k$| forms the betweenness centrality profile of a vertex. We study properties of betweenness centrality profiles in trees.
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