Wigner-noise on random matrices with remarkable linear structure (applicable to cellular networks)

Spectra and representations of some special weighted graphs are investigated with weight matrices consisting of homogeneous blocks. It is proved that a random perturbation of the weight matrix with a "Wigner-noise" will not have an effect on the order of the protruding eigenvalues and the representatives of the vertices will unveil the underlying block-structure. Such random graphs adequately describe some biological and communication networks, the vertices of which belong either to loosely connected strata or to clusters with homogeneous edge-densities between any two of them.