Abstract
‘Connected and close’ shows almost all the elements of networks take part in one large connected structure, called a giant connected component. Almost every node has a path of connections with every other, but these paths are extremely short: networks tend to be sparse rather than dense. This is shown clearly by psychologist Stanley Milgram's ‘six degrees of separation’ experiment. This small-world property is present in all networks. How is a network different from a grid? No real network is an ordered array of elements. Instead, there is always disorder. The interwoven structure in networks is essential to understanding a broad range of phenomena, from Aids to blackouts to information spreading.
