Recognizing linear structure in noisy matrices

Behaviour of the eigenvalues of random matrices with an underlying linear structure is investigated, when the structure is exposed to random noise. The question, how a deterministic skeleton behind a random matrix can be recognized, is also discussed. Such random matrices, as weight matrices of random graphs, adequately describe some large biological and communication networks. A range for the power of random power law graphs-for which the structure is robust enough-is established.