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We consider the canonical ensemble of -vertex Erdős-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity for each closed triple of bonds. We claim complete defragmentation of large- graphs into the collection of almost full subgraphs (cliques) above critical fugacity, , where is the ER bond formation probability. Evolution of the spectral density, , of the adjacency matrix with increasing leads to the formation of a multizonal support for . Eigenvalue tunneling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a block-diagonal form, where the number of vertices in blocks fluctuates around the mean value . The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional …