To learn more about the behavior of networks and their abilities to be modeled and studied, I've downloaded Gephi, a graph exploration & manipulation tool.

At Gephi.org, they call this kind of work Dynamic Network Analysis (DNA), and they've created a development platform that can be used to visualize networks. They also have an informative documentary about the "Six degrees of separation" concepts, including great background material about the trivia game called "Six Degrees of Kevin Bacon", and what has come from all of the exciting realizations that have pointed us towards important scientific breakthroughs in how we understand why Everything Is Connected to Everything Else.