Rumour spreading on graphs

How does gossip spread? How do technologies diffuse within or across societies? How do fads and fashions take hold? How do people learn about job opportunities or recruit workers? All these are examples of information spread over social networks, networks of friendship, family and acquaintance. They play a role in everything from the smooth functioning of economies to the maintenance of social and cultural groupings. Those are some of the questions that motivate our study of rumour/information spread in networks. Another motivation comes from synthetic networks like the Internet or peer-to-peer networks, where it may be important to disseminate information rapidly; for example, security updates or routing tables. Rumour spreading mechanisms provide a template for many distributed algorithms on such networks. In these lectures, we shall look at some highly simplified mathematical models of information spread, with the goal of addressing precise questions about the spped of spread. But first, we familiarise ourselves with some terminology.