Abstract. Complex networks typically have the following properties:
(A1) The number of edges is in O(n ln n).
(A2) The diameter is in O(ln n).
(A3) The clustering coefficient is greater than a positive constant.
(A4) The proportion of vertices of degree at least k is approximalely equal to k1-t, where t is usually between 2 and 3.
(A5) The network is self-similar.

Using very symmetric graphs we generalize several deterministic self-similar models of complex networks. Then we calculate the order, size, degree distribution, we give an upper bound for the diameter and the lower bound for the clustering coefficient of our generalization. As a consequence, we can model complex networks with prescribed properties, which we demonstrate on the clustering coefficient. In the paper we give 8 new infinite classes of complex networks.