Evolving Complex Networks

The Ising model we studied in an earlier chapter was based on a fixed number of nodes (the place where the spins or agents are located) interacting on a network of fixed topology, that is, the links among the agents was also fixed. More realistic complex systems in the social or biological world involve a change in the number of agents and also the links among them. In the previous section we encountered a case in which though the number of nodes is fixed, the links evolve dynamically. The next generalization involves allowing also the number of nodes to change. An example of such a network would be the world-wide-web (WWW) whose nodes are html documents with links pointing from one node to another. Another evolving network is the collaboration diagram of movie stars. These and other interesting applications of complex networks, such as the ``six degrees of separation" phenomena (``its a small world" phenomenon), are discussed in Refs.[18,19].