Exact formula for bond percolation on cliques

We present exact solutions for the size of giant connected component (GCC) graphs composed higher-order homogeneous cycles, including weak cycles and cliques, following bond percolation. use our theoretical result to find location percolation threshold model, providing analytical where possible. expect results derived here be useful a wide variety applications graph theory, epidemiology, lattice gas models as well fragmentation theory. also examine Erd\H{o}s-Gallai theorem necessary condition on graphicality configuration model networks comprising clique sub-graphs.