2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208162Complex 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 $M_N(h) \sim (\ln N)^ψ$, respectively. This classification coincides with the one according to the percolation critical phenomena.4 pages and 2 figures; A major revision has been madeStatistical Mechanicstext