  We consider the canonical ensemble of $N$-vertex Erd\H{o}s-R\'enyi (ER)
random topological graphs with quenched vertex degree, and with fugacity $\mu$
for each closed triple of bonds. We claim complete defragmentation of large-$N$
graphs into the collection of $[p^{-1}]$ almost full subgraphs (cliques) above
critical fugacity, $\mu_c$, where $p$ is the ER bond formation probability.
Evolution of the spectral density, $\rho(\lambda)$, of the adjacency matrix
with increasing $\mu$ leads to the formation of two-zonal support for
$\mu>\mu_c$. Eigenvalue tunneling from one (central) zone to the other means
formation of a new clique in the defragmentation process. The adjacency matrix
of the ground state of a network has the block-diagonal form where number of
vertices in blocks fluctuate around the mean value $Np$. The spectral density
of the whole network in this regime has triangular shape. We interpret the
phenomena from the viewpoint of the conventional random matrix model and
speculate about possible physical applications.
