  The effects of link rewiring are considered for the class of directed
networks where each node has the same fixed out-degree. We model a network
generated by three mechanisms that are present in various networked systems;
growth, global rewiring and local rewiring. During a rewiring phase a node is
randomly selected, one of its out-going edges is detached from its destination
then re-attached to the network in one of two possible ways; either globally to
a randomly selected node, or locally to a descendant of a descendant of the
originally selected node. Although the probability of attachment to a node
increases with its connectivity, the probability of detachment also increases,
the result is an exponential degree distribution with a small number of
outlying nodes that have extremely large degree. We explain these outliers by
identifying the circumstances for which a set of nodes can grow to very high
degree.
