Analysis of Complex Networks

10.1 Introduction

Nervous systems are complex networks par excellence, capable of generating and integrating information from multiple external and internal sources. Within the neuroanatomical network (structural connectivity), the nonlinear dynamics of neurons and neuronal populations result in patterns of statistical dependencies (functional connectivity) and causal interactions (effective connectivity), defining three major modalities of complex brain networks [61]. How does the structure of the network relate to its function and what effect do changes of edge or node properties have [37]? Since 1992 [1,76] tools from graph theory and network analysis [18] have been applied to study these questions in neural systems (cf. http://www.biological-networks.org).

After describing the properties of neural systems – fiber tracts between brain areas of the mammalian cortex and axons between individual neurons in the nematode Caenorhabditis elegans–wedescribedynamicsin structure and function. Structural dynamics concern changes in network topology by deleting or adding edges or nodes. We describe the deletion of components in terms of the removal of tissue during strokes or head injuries and the addition of components during the development and growth of neural systems. The network topology is robust to random attacks but reacts critically to targeted attacks – similar to a scale-free network. The simulations on network evolution show that spatial growth and time windows during development ...