There is no sharp border between structural transformations of networks and cooperative models using networks as a substrate. I will discuss both these issues. Standard random graph constructions will be outlined. Mechanisms (equations) which lead to the emergence of complex networks will be described. It will be demonstrated how the combination of two features – D=¥ and complex distribution of connections – results in unusual critical behaviours of cooperative models on networks.

A.F. Ioffe Physico-Technical Institute, St. Petersbourg and SPhT