Synchronization in networks with different topologies is studied. We show that for a large class of oscillators there exist two classes of networks; class-A: networks for which the condition of stable synchronous state is σγ2 > a, and class-B: networks for which this condition reads γN/γ2 < b, where a and b are constants that depend on local dynamics, synchronous state and the coupling matrix, but not on the Laplacian matrix of the graph describing the topology of the network. Here γ1 = 0 < γ2 < . . . < γN are the eigenvalues of the Laplacian matrix, where N is the order of the graph. Synchronization in networks whose topology is described by classical random graphs and power-law random graphs when N → ∞ is investigated in detail.