  We introduce a correlated static model and investigate a percolation
transition. The model is a modification of the static model and is
characterized by assortative degree-degree correlation. As one varies the edge
density, the network undergoes a percolation transition. The percolation
transition is characterized by a weak singular behavior of the mean cluster
size and power-law scalings of the percolation order parameter and the cluster
size distribution in the entire non-percolating phase. These results suggest
that the assortative degree-degree correlation generates a global structural
correlation which is relevant to the percolation critical phenomena of complex
networks.
