Analysis of Complex Networks

10.4 Summary

Using methods and concepts of network analysis [4], we discussed the topological organization and structural and functional dynamics of neural networks. The topology of neural systems is influenced by several constraints: the specialization into different subsystems such as modules for visual, auditory, or sensorimotor processing leads to topological clusters in cortical networks [34] or multiple ganglia for the neuronal network of C. elegans. However, not all connections are limited to the local neighborhood of individual modules: several spatially long-distance connections exist for both integrating different processing streams as well as enabling rapid processing due to reduction in the characteristic path length (analogously to shortcuts in small-world networks) [43]. Cortical networks show maximal structural and dynamic complexity, which is thought to be necessary for encoding a maximum number of functional states and might arise as a response to rich sensory environments [63]. Sporns and Kötter [62] have looked at how the structure links to the degrees of freedom for network function. Motif analysis of cortical (macaque) and neuronal (C. elegans) systems shows that these systems are optimized for a maximal number of possible functional motifs over the total network where the number of functional motifs of one structural motif is the set of distinct configurations of activated edges. More recent results concern frequency patterns [53] and synchronization [23] ...