  Node betweenness has been studied recently by a number of authors, but until
now less attention has been paid to edge betweenness. In this paper, we present
an exact analytic study of edge betweenness in evolving scale-free and
non-scale-free trees. We aim at the probability distribution of edge
betweenness under the condition that a local property, the in-degree of the
``younger'' node of a randomly selected edge, is known. En route to the
conditional distribution of edge betweenness the exact joint distribution of
cluster size and in-degree, and its one dimensional marginal distributions have
been presented in the paper as well. From the derived probability distributions
the expectation values of different quantities have been calculated. Our
results provide an exact solution not only for infinite, but for finite
networks as well.
