The authors look at the evolution of a fixed size preferential attachment random graph model which is based on the Gaian database. It is well known that the model starts out scale-free. However, they show that as the graph evolves it loses this scale-free nature and becomes more regular as nodes leave and enter the network. This change in characteristic will impact the performance of queries within a Gaian DataBase (GDB) network. They show that this happens for a wide variety of related models and the impact of capping the number of connections per node is considered.