  We introduce a collection of complex networks generated by a combination of
preferential attachment and a previously unexamined process of "splitting"
nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered,
each evolves at each time step by either preferential attachment, with
probability $p$, or splitting with probability $1-p$. Two methods of attachment
are considered; first, attachment of an edge between a newly created node and
existing node in the network, and secondly by attachment of an edge between two
existing nodes. Splitting is also considered in two separate ways; first by
selecting each node with equal probability and secondly, selecting the node
with probability proportional to its degree. Exact solutions for the degree
distributions are found and scale-free structure is exhibited in those networks
where the candidates for splitting are chosen with uniform probability, those
that are chosen preferentially are distributed with a power law with
exponential cut-off.
