  Betweenness centrality is a measure of the importance of a vertex x inside a
network based on the fraction of shortest paths passing through x. We study a
blow-up construction that has been shown to produce graphs with uniform
distribution of betweenness. We disprove the conjecture about this procedure's
universality by showing that trees with a diameter at least three cannot be
transformed into betweenness-uniform by the blow-up construction. It remains
open to characterize graphs for which the blow-up construction can produce
betweenness-uniform graphs.
