New approaches to the random generation of combinatorial objects

Networks are useful theoretical combinatorial objects, and also occur in natural contexts, such as social networks,
the network of the world wide web, and so on. Some studies require simulations, and often the best option is to
generate the networks uniformly at random. Then each one of a given size occurs with the same probability. This
proposal will introduce revolutionary approaches to performing this task, enabling it to be done efficiently for a
much broader range of many important classes of networks, graphs and other combinatorial objects than before.
This will permit better simulations, as well as efficient and truthful sampling, giving better prediction of network
properties and better analysis of algorithms applied to networks.