Complex networks and activity spreading

We give a brief survey of the basic notions of the theory of complex networks and various models of activity spreading in networks. We consider the role of random graph theory for the study of complex networks, describe small world and scale-free networks, activity spreading models in social networks, percolation processes, the concept of self-organized criticality, and two versions of its formalization: cellular automata and the chip firing game. We note the common elements of all considered models.