In this work we study the structural changes in neuronal networks emerging during network maturation. We analyze two computational models proposed in the literature that describe the growth of neurons. The models have planar geometry and the density of cells is chosen to correspond to the ’dense’ and ’sparse’ cultures reported in the experimental studies. The growth of the model neurons and networks is simulated using two novel publicly available simulators. A graph representation of the networks is obtained from the simulation results and examined at days 7, 14, and 21. The two models are clearly different in nature. The first can model large networks phenomenologically, while the second describes some of the relevant biophysical processes in smaller networks. The difference in modeling approach is evident in the graph properties.