A noble and ultimate objective of phyloinformatic research is to assemble, synthesize, and explore the evolutionary history of life on earth. Data mining methods for performing these tasks are not yet well developed, but one avenue of research suggests that network connectivity dynamics will play an important role in future methods. Analysis of disordered networks, such as small-world networks, has applications as diverse as disease propagation, collaborative networks, and power grids. Here we apply similar analyses to networks of phylogenetic trees in order to understand how synthetic information can emerge from a database of phylogenies.