Evolving networks and the development of neural systems

It is now generally assumed that the heterogeneity of most networks in nature probably arises via preferential attachment of some sort. However, the origin of various other topological features, such as degree-degree correlations and related characteristics, is often not clear, and they may arise from specific functional conditions. We show how it is possible to analyse a very general scenario in which nodes can gain or lose edges according to any (e.g., nonlinear) function of local and/or global degree information. Applying our method to two rather different examples of brain development - synaptic pruning in humans and the neural network of the worm C.Elegans - we find that simple biologically motivated assumptions lead to very good agreement with experimental data. In particular, many nontrivial topological features of the worm's brain arise naturally at a critical point.