Complex Dynamical Networks

Description

In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in graphs modelling of real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by the empirical study of real-world networks such as Computer Networks, technological networks, brain networks and Social Networks. - From Wikipedia, the free encyclopedia

This course covers theory and modeling of real-world networks such as computer, social, and biological networks where the underlying topology is a dynamically growing complex graph. Many phenomena in nature can be modeled as a network. Researchers from many areas including computer science, engineering, epidemiology, mathematics, physics, and biology have been studying complex networks of their field. Scale-free networks and small-world networks are well known examples of complex networks. These networks have been identified in many fundamentally different systems.

Network is named scale-free, if its degree distribution, i.e., the probability that a node selected uniformly at random has a certain number of links (degree), follows a particular mathematical function called a power law. The power law implies that the degree distribution of these networks has no characteristic scale.

A network is called a small-world network by analogy with the small-world phenomenon (popularly known as six degrees of separation). The small world hypothesis, which was first described by the Hungarian writer Frigyes Karinthy in 1929, and tested experimentally by Stanley Milgram (1967), is the idea that two arbitrary people are connected by only six degrees of separation, i.e. the diameter of the corresponding graph of social connections is not much larger than six. In 1998, Duncan J. Watts and Steven Strogatz published the first small-world network model, which through a single parameter smoothly interpolates between a random graph and a lattice.

Lectures