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We compute analytically the distribution and moments of the largesteigenvalues/singular values and resolvent statistics for random matrices with(i) non-negative entries, (ii) small rank, and (iii) prescribed sums ofrows/columns. Applications are discussed in the context of Mean First PassageTime of random walkers on networks, and the calculation of network "influence"metrics. The analytical results are corroborated by numerical simulations.

Statistics of the largest eigenvalues and singular values of low-rank random matrices with non-negative entries