  Complex networks display various types of percolation transitions. We show
that the degree distribution and the degree-degree correlation alone are not
sufficient to describe diverse percolation critical phenomena. This suggests
that a genuine structural correlation is an essential ingredient in
characterizing networks. As a signature of the correlation we investigate a
scaling behavior in $M_N(h)$, the number of finite loops of size $h$, with
respect to a network size $N$. We find that networks, whose degree
distributions are not too broad, fall into two classes exhibiting $M_N(h)\sim
({constant})$ and $M_N(h) \sim (\ln N)^\psi$, respectively. This classification
coincides with the one according to the percolation critical phenomena.
