  We analyze the betweenness centrality (BC) of nodes in large complex
networks. In general, the BC is increasing with connectivity as a power law
with an exponent $\eta$. We find that for trees or networks with a small loop
density $\eta=2$ while a larger density of loops leads to $\eta<2$. For
scale-free networks characterized by an exponent $\gamma$ which describes the
connectivity distribution decay, the BC is also distributed according to a
power law with a non universal exponent $\delta$. We show that this exponent
$\delta$ must satisfy the exact bound $\delta\geq (\gamma+1)/2$. If the scale
free network is a tree, then we have the equality $\delta=(\gamma+1)/2$.
