I find it interesting to note the difference between the graph theory and the topological definitions of connectedness when we apply both to society.
The graph theory definition means that people are connected with things, such as phonelines.
The definition given by topology is far more thought provoking. Society is divided into sets. To make things interesting, lets consider one partition based on culture. Is society connected? For this to be true, society cannot be decomposed into a set of disjoint subsets. This is to say that in each culture, there must be a member who is also a member of some other culture. In other words, for society to be topologically connected, every culture must contain people who are "poly-cultural". This was certainly untrue back in the days when society was disconnected in the graph theory sense, but I would like to postulate that a result of connectedness in the first sense will be connectedness in the second sense, eventually giving rise to a global village.