Visualizing complex networks

Theoretical foundations of network analysis have traditionally been studied in graph theory. Numerous graph-theoretical algorithms have been developed and used in solving a variety of problems. Recently, networks have become a central topic of research in theoretical physics, especially statistical physics. A number of concepts have played key roles in the latest proliferation of such studies, including small-world networks and scale-free networks. Many underlying phenomena studied by physicists are known as non-linear systems because a linear relationship between the input and the output, or between a cause and its effect, does not exist.Mathematically, a power law is one of the most commonly used methods to describe such relationships. Researchers are particularly interested in two types of dynamics in complex networks: (1) event-driven processes, a dynamic process is apparently caused by external interferences, for instance, a snow avalanche caused by a storm; (2) self-organized criticality, a system in which dramatic changes may take place in the absence of major causes at the macroscopic level.Many of the studies in the current complex network theory have not yet reached a level that one can specifically identify the cause-effect relations associated with the dynamics observed over a complex network. There is considerable evidence, however, to believe that the ability to distinguish the two types of dynamic processes in the near future will lead to much more insights into complex networks.