Network Theory

Dynamical and adaptive networks are the backbone of many complex systems. Examples range from ecological prey–predator networks to the gene expression and protein providing the grounding of all living creatures. The basis of our own identity is provided by the highly sophisticated neural network we carry in our heads. On a social level we interact through social and technical networks like the Internet. Networks are ubiquitous throughout the domain of all living creatures. A good understanding of network theory is of basic importance for complex systems theory. In this chapter we will discuss the most important notions of graph theory, like clustering and degree distributions, together with basic network realizations. Central concepts like percolation, the robustness of networks with regard to failure and attacks, and the “rich-get-richer” phenomenon in evolving social networks will be treated.