Many real systems (Internet, biological and social systems, neuron networks and etc.) are random complex networks with a peculiar network topology. We discuss architecture and properties of real complex networks. We consider the robustness of complex networks against random damages (the percolation threshold) and the infection spreading in networks. In the framework of the generalized Landau theory we discuss the influence of the network topology on the critical behavior at an order-disorder phase transition in complex networks.

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