This animation shows you everything that a network is and everything it can do. It is made up of just two kinds of things: nodes and links. Everything a network does emerges from the patterns made by the linking of the nodes.
Not until the end of the 20th century was it realized that networks are not just regular (like fishnets) or random (with no rhyme or reason). Networks, it is now known can express any conceivable reason or rhyme.
Come to think of it, living brains are the same way: they are networks. The internet is the first network medium into which we have been able to place all our human reasons and rhymes. A book is linear — though it can get your brain to network ideas as you read it.
The rhymes and reasons — math, sciences, humanities and the rest — that are used in education should be used by teachers and students from the new networked medium. You have probably noticed that in the animation above, you can think of the nodes as individual people. Social networking emerges patterns of people. Education should be reconfigured around making sure a person who is a learning node can link to a node in the online pattern of what she is studying.